Although I'm not sure why anyone would give any credibility to what Paul VI or JXXIII may have said given they were the ones who foisted this horror on us, I do get that believing this was just "pastoral" in nature helps certain Catholics sleep better at night.
No reason to assume they were lying. The Church is under the protection of the Holy Spirit. The novelties promoted by VII (intended to change the culture of the Church rather than define doctrine) conflict with Tradition. Neither Popes nor councils are empowered by God to contravene the Deposit of Faith. And Paul VI did not have the right to abrogate the Mass canonized by Pope St. Pius V, so he attempted to suppress it via praxis. The "pastoral" aberrations promoted by VII are not binding because they conflict with the Deposit of Faith.
"...According to the General Secretary of Vatican II, distinctions must be made: the dogmatic definitions of the past must of course be adhered to, but “reservations” must be made regarding any doctrines of a “novel character”. Never before in the history of the Catholic Church had a council ever taken pains to declare that it was not teaching infallibly, unless it should “openly declare so”, which it never did. And that a General Secretary should confide that “reservations” must be made about its teachings of “a novel character” is quite staggering. Vatican II was clearly unlike any ecumenical council which preceded it..."
http://www.romancatholicism.org/vatican-ii.html
"...As one can see, here too Paul VI expressly declared that Vatican II did not intend to teach, through dogmatic definitions, any Chapterof doctrine, and therefore, necessarily, Vatican II is in no part covered by infallibility, since infallibility is tied only to the “truths” taught by the Universal Ordinary Magisterium as revealed – and, therefore, to be believed “de fide divina”, aut “catholica” – by the Solemn Magisterium and by the Ecumenical Councils, or even by the Supreme Pontiff, as regards dogmatic definitions..."
http://padrepioandchiesaviva.com/uploads/Paul_VI.._beatified_english.pdf