In rebuttal, I have always pointed these folks to Lumen Gentium 14 which says:
14. This Sacred Council wishes to turn its attention firstly to the Catholic faithful. Basing itself upon Sacred Scripture and Tradition, it teaches that the Church, now sojourning on earth as an exile, is necessary for salvation. Christ, present to us in His Body, which is the Church, is the one Mediator and the unique way of salvation. In explicit terms He Himself affirmed the necessity of faith and baptism(124) and thereby affirmed also the necessity of the Church, for through baptism as through a door men enter the Church. Whosoever, therefore, knowing that the Catholic Church was made necessary by Christ, would refuse to enter or to remain in it, could not be saved.
They are fully incorporated in the society of the Church who, possessing the Spirit of Christ accept her entire system and all the means of salvation given to her, and are united with her as part of her visible bodily structure and through her with Christ, who rules her through the Supreme Pontiff and the bishops. The bonds which bind men to the Church in a visible way are profession of faith, the sacraments, and ecclesiastical government and communion. He is not saved, however, who, though part of the body of the Church, does not persevere in charity. He remains indeed in the bosom of the Church, but, as it were, only in a "bodily" manner and not "in his heart."(12*) All the Church's children should remember that their exalted status is to be attributed not to their own merits but to the special grace of Christ. If they fail moreover to respond to that grace in thought, word and deed, not only shall they not be saved but they will be the more severely judged.(13*)
Catechumens who, moved by the Holy Spirit, seek with explicit intention to be incorporated into the Church are by that very intention joined with her. With love and solicitude Mother Church already embraces them as her own.
124 Cf. Mc 16, 16; Jn. 3, 5.
(12*) Cfr. S. Augustinus, Bapt. c. Donat. V, 28, 39; PL 43, 197: Certe manifestum est, id quod dicitur, in Ecdesia intus et foris, in corde, non in corpore cogitandum. Cfr. ib., III, 19, 26: col. 152; V, 18, 24: col. 189; In Io. Tr. 61, 2: PL 35, 1800, et alibi saepe.
(13*) Cfr. Lc. 12, 48: Omni autem, cui multum datum est, multum quaeretur ab eo. Cfr. etiam Mt. 5, 19-20; 7, 21-22; 25 41-46; Iac., 2, 14.
But like good prots, they do the same thing to the Documents of VCII that they do to Scripture: they ignore the parts of VCII that do not meet their preconcieved conclusions.
When the document Dominus Iesus was promulgated back in 2000, we had another spurt of criticisms by the unlettered who claimed that it "reversed" the teaching of VCII. But in fact it reitereted what LG 14 had said:
16. The Lord Jesus, the only Saviour, did not only establish a simple community of disciples, but constituted the Church as a salvific mystery: he himself is in the Church and the Church is in him (cf. Jn 15:1ff.; Gal 3:28; Eph 4:15-16; Acts 9:5). Therefore, the fullness of Christ's salvific mystery belongs also to the Church, inseparably united to her Lord. Indeed, Jesus Christ continues his presence and his work of salvation in the Church and by means of the Church (cf. Col 1:24-27),(47) which is his body (cf. 1 Cor 12:12-13, 27; Col 1:18).(48) And thus, just as the head and members of a living body, though not identical, are inseparable, so too Christ and the Church can neither be confused nor separated, and constitute a single “whole Christ”.(49) This same inseparability is also expressed in the New Testament by the analogy of the Church as the Bride of Christ (cf. 2 Cor 11:2; Eph 5:25-29; Rev 21:2,9).(50)
Therefore, in connection with the unicity and universality of the salvific mediation of Jesus Christ, the unicity of the Church founded by him must be firmly believed as a truth of Catholic faith. Just as there is one Christ, so there exists a single body of Christ, a single Bride of Christ: “a single Catholic and apostolic Church”.(51) Furthermore, the promises of the Lord that he would not abandon his Church (cf. Mt 16:18; 28:20) and that he would guide her by his Spirit (cf. Jn 16:13) mean, according to Catholic faith, that the unicity and the unity of the Church — like everything that belongs to the Church's integrity — will never be lacking.(52) The Catholic faithful are required to profess that there is an historical continuity — rooted in the apostolic succession (53) — between the Church founded by Christ and the Catholic Church: “This is the single Church of Christ... which our Saviour, after his resurrection, entrusted to Peter's pastoral care (cf. Jn 21:17), commissioning him and the other Apostles to extend and rule her (cf. Mt 28:18ff.), erected for all ages as ‘the pillar and mainstay of the truth' (1 Tim 3:15). This Church, constituted and organized as a society in the present world, subsists in [subsistit in] the Catholic Church, governed by the Successor of Peter and by the Bishops in communion with him”.(54) With the expression subsistit in, the Second Vatican Council sought to harmonize two doctrinal statements: on the one hand, that the Church of Christ, despite the divisions which exist among Christians, continues to exist fully only in the Catholic Church, and on the other hand, that “outside of her structure, many elements can be found of sanctification and truth”,(55) that is, in those Churches and ecclesial communities which are not yet in full communion with the Catholic Church.(56) But with respect to these, it needs to be stated that “they derive their efficacy from the very fullness of grace and truth entrusted to the Catholic Church”.(57 )
17. Therefore, there exists a single Church of Christ, which subsists in the Catholic Church, governed by the Successor of Peter and by the Bishops in communion with him.(58) The Churches which, while not existing in perfect communion with the Catholic Church, remain united to her by means of the closest bonds, that is, by apostolic succession and a valid Eucharist, are true particular Churches.(59) Therefore, the Church of Christ is present and operative also in these Churches, even though they lack full communion with the Catholic Church, since they do not accept the Catholic doctrine of the Primacy, which, according to the will of God, the Bishop of Rome objectively has and exercises over the entire Church....(60)
22. With the coming of the Saviour Jesus Christ, God has willed that the Church founded by him be the instrument for the salvation of all humanity (cf. Acts 17:30-31).(90) This truth of faith does not lessen the sincere respect which the Church has for the religions of the world, but at the same time, it rules out, in a radical way, that mentality of indifferentism “characterized by a religious relativism which leads to the belief that ‘one religion is as good as another'”.(91) If it is true that the followers of other religions can receive divine grace, it is also certain that objectively speaking they are in a gravely deficient situation in comparison with those who, in the Church, have the fullness of the means of salvation.(92) However, “all the children of the Church should nevertheless remember that their exalted condition results, not from their own merits, but from the grace of Christ. If they fail to respond in thought, word, and deed to that grace, not only shall they not be saved, but they shall be more severely judged”.(93) One understands then that, following the Lord's command (cf. Mt 28:19-20) and as a requirement of her love for all people, the Church “proclaims and is in duty bound to proclaim without fail, Christ who is the way,
the truth, and the life (Jn 14:6). In him, in whom God reconciled all things to himself (cf. 2 Cor 5:18-19), men find the fullness of their religious life”.(94)
(47) Cf. Second Vatican Council, Dogmatic Constitution Lumen
(48) Cf. ibid., 7.
(49) Cf. St. Augustine, Enarratio in Psalmos, Ps. 90, Sermo 2,1: CCSL 39, 1266; St. Gregory the Great, Moralia in Iob, Praefatio, 6, 14: PL 75, 525; St. Thomas Aquinas, Summa Theologiae, III, q. 48, a. 2 ad 1.
(50) Cf. Second Vatican Council, Dogmatic Constitution Lumen
(51) Symbolum maius Ecclesiae Armeniacae: DS 48. Cf. Boniface VIII, Unam sanctam: DS 870-872; Second Vatican Council, Dogmatic Constitution Lumen gentium, 8.
(52) Cf. Second Vatican Council, Decree Unitatis redintegratio,
4; John Paul II, Encyclical Letter Ut unum sint, 11: AAS 87 (1995), 927.
(53) Cf. Second Vatican Council, Dogmatic Constitution Lumen Gentium, 20; cf. also St. Irenaeus, Adversus haereses, III, 3, 1-3: SC 211,
20-44; St. Cyprian, Epist. 33, 1: CCSL 3B, 164-165; St. Augustine, Contra adver. legis et prophet., 1, 20, 39: CCSL 49, 70.
(54) Second Vatican Council, Dogmatic Constitution Lumen
(55) Ibid.; cf. John Paul II, Encyclical Letter Ut unum sint, 13. Cf. also Second Vatican Council, Dogmatic Constitution Lumen gentium, 15 and the Decree Unitatis redintegratio, 3.
(56) The interpretation of those who would derive from the formula subsistit in the thesis that the one Church of Christ could subsist also in non-Catholic Churches and ecclesial communities is therefore contrary to the authentic meaning of Lumen gentium. “The Council instead chose the word subsistit precisely to clarify that there exists only one ‘subsistence' of the true Church, while outside her visible structure there only exist elementa Ecclesiae, which — being elements of that same Church — tend and lead toward the Catholic Church” (Congregation for the Doctrine of the Faith, Notification on the Book “Church: Charism and Power” by Father Leonardo Boff: AAS 77 , 756-762).
(57) Second Vatican Council, Decree Unitatis redintegratio, 3.
(58) Cf. Congregation for the Doctrine of the Faith, Declaration Mysterium Ecclesiae, 1: AAS 65 (1973), 396-398.
(59) Cf. Second Vatican Council, Decree Unitatis redintegratio,
14 and 15; Congregation for the Doctrine of the Faith, Letter Communionis notio, 17: AAS 85 (1993), 848.
(60) Cf. First Vatican Council, Constitution Pastor aeternus: DS 3053-3064; Second Vatican Council, Dogmatic Constitution Lumen gentium, 22.
(90) Cf. Second Vatican Council, Dogmatic Constitution Lumen
Gentium, 17; John Paul II, Encyclical Letter Redemptoris missio, 11.
(91) John Paul II, Encyclical Letter Redemptoris missio, 36.
(92) Cf. Pius XII, Encyclical Letter Mystici corporis: DS 3821.
(93) Second Vatican Council, Dogmatic Constitution Lumen
(94) Second Vatican Council, Declaration Nostra aetate, 2.
But they were STILL not persuaded, and I was open to more vilification.
Well, now we have the new document "Responses to Some Questions Regarding Certain Aspects of the Doctrine on the Church" which leaves no doubt as to what the Catholic Church teaches on this matter. In particular:
What is the meaning of the affirmation that the Church of Christ subsists in the Catholic Church?
Christ “established here on earth” only one Church and instituted it as a “visible and spiritual community”, that from its beginning and throughout the centuries has always existed and will always exist, and in which alone are found all the elements that Christ himself instituted. “This one Church of Christ, which we confess in the Creed as one, holy, catholic and apostolic […]. This Church, constituted and organised in this world as a society, subsists in the Catholic Church, governed by the successor of Peter and the Bishops in communion with him”.
In number 8 of the Dogmatic Constitution Lumen Gentium ‘subsistence’ means this perduring, historical continuity and the permanence of all the elements instituted by Christ in the Catholic Church, in which the Church of Christ is concretely found on this earth.
It is possible, according to Catholic doctrine, to affirm correctly that the Church of Christ is present and operative in the churches and ecclesial Communities not yet fully in communion with the Catholic Church, on account of the elements of sanctification and truth that are present in them. Nevertheless, the word "subsists” can only be attributed to the Catholic Church alone precisely because it refers to the mark of unity that we profess in the symbols of the faith (I believe... in the “one” Church); and this “one” Church subsists in the Catholic Church.
 Cf. Second Vatican Council, Dogmatic Constitution Lumen Gentium, 8.1.
 Cf. Congregation for the Doctrine of the Faith, Declaration Mysterium Ecclesiae, 1.1: AAS 65  397; Declaration Dominus Iesus, 16.3: AAS 92 [2000-II] 757-758; Notification on the Book of Leonardo Boff, OFM, “Church: Charism and Power”: AAS 77  758-759.
So to all of those people who have given me grief over the years and told me that I did not understand the teaching of my own Catholic Church: I TOLD YOU SO!