Yes, Stanley, this is Archbishop Lefebvre, from Michael Davies' Apologia: "And so, far from refusing to pray for the Pope, we redouble our prayers and supplications that the Holy Ghost will grant him light and strength in his affirmations and defense of the Faith. Thus, I have never refused to go to Rome at his request or that of his representatives. The Truth must be affirmed at Rome above all other places. It is of God, and He will assure its ultimate Triumph. Consequently, the Society of St. Pius X, its Priests, Brothers, Sisters, and Oblates, cannot tolerate among its members those who refuse to pray for the Pope or affirm that the Novus Ordo Missae is per se invalid." https://www.sspxasia.com/Documents/Archbishop-Lefebvre/Apologia/Vol_two/Chapter_40.htm
And this is the article I was talking about, from Salza and Siscoe, whose recent book True or False Pope btw was approved and authorized for publication by SSPX Bishops and Priests including, I think, Bp. Fellay and Fr. Laisney. I know Fr. Therasian Xavier also wrote a positive review of it: “The answer here is similar to the preceding. Prior to the election, there is a moral certainty that all these conditions required in the person are actually met. After the fact of the election and its acceptance, the fulfillment of these conditions is known with the certainty of a theological conclusion, since they have, per se, a logical implication with a truth that is certain, and certified by faith. (…) the truth that is defined and accepted by the Church is not that this man is baptized or ordained, etc., but that this man is truly pope. (…) That he is baptized and meets the other requirements [i.e., that he is not a public heretic] … is inferred as a consequence; (…) the truth that this man has been ordained, and has the power of order (that is, of the priesthood or episcopate), is certain in the same way as the truth that he is baptized is certain; namely, not as a truth immediately de fide, but as a theological conclusion necessarily connected with the truth that he is the Pope and the rule of faith in the Church." https://gloria.tv/article/PydgSw3mJAWF2w9rLGgxGBa4h
Therefore, since it is certain by the fact of universal acceptance that Pope Benedict XVI is Pope, it follows that the new rite of episcopal consecration cannot be per se invalid. And since Pope Francis was elected and accepted as Pope after that, the same follows for the new rite of ordination - it cannot be per se invalid. That is all.
When it comes to Novus Ordo sacraments, another problem is the Holy Oils used. Those sacraments which depend on proper, valid Holy Oils suffer because of a change Paul VI made. He allowed vegetable oils to be used in place of olive oil. Ihsv, yes, each of the four have to be considered, (1) Matter, (2) Form, (3) Minister (4) Intention. The argument is simply, if the new rites are always invalid, the Church of Rome has defected, with no valid episcopal lineage, and no residential Bishop, which is impossible. Therefore, the form of the new rite, when used with proper intention, and accompanying matter (the oils for Sacraments like Confirmation etc) are certainly not (even more than moral certainty, this is certainty closely connected with truths of Faith, as John of St. Thomas explains) per se invalid. This solid theoretical conclusion affects the praxis the Society follows in receiving Bishops from the mainstream Church who come over to the Society. The background is closely investigated for any defects of matter and of intention, keeping in mind the principles established earlier. If none are found after a careful investigation from the Episcopal authorities of the Society, the Bishop is welcomed. Laymen wish to protest this today, but imho, it's safe and sure to follow the judgment of the Superior General on such matters. A statement of St. Ignatius of Antioch, concerning the Bishop's role in administering and guaranteeing the validity of the Sacraments in such matters, could be applied here, "Let no man do anything connected with the Church without the Bishop ... whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid."
This is why Traditional Catholicism exists and is the ONLY reason we can exist, both legally and morally.
No, this is false. Summorum Pontificum and Universae Ecclesiae disagree with you. Every Bishop and Priest has the right to use all the traditional rites. I've already explained using the analogy of Baptism how a rite can be weakened (theologians distinguish integrity and essence) without compromising validity. This weakening leads to a massive loss of grace and that loss of grace is sufficient reason not to use the new rites, but “without any rebellion, bitterness, or resentment, we pursue our work of Priestly formation under the guidance of the never-changing Magisterium, convinced as we are that we cannot possibly render a greater service to the Holy Catholic Church, to the Sovereign Pontiff, and to posterity.” (Bp. Fellay), we can legitimately continue to use all the traditional rites, since they give greater glory to God, and obtain for us super-abundantly the grace and sanctification we need to save our souls, and that the Church and the world desperately need more abundantly. Protestants may baptize wrongly (i.e. by omitting the ceremonies that accompany the essential form, as when it is rightly administered in the Catholic Church, by Traditional Priests), but we will not. Neither need we deny the validity of their Baptism to do so.
You claim other rites are different, but that is not true - Catholic Sacramental Theology is that each and every Sacrament is validly conferred by the essential form - even Abp. Lefebvre wrote above, "- that the Sacrifice and the Sacrament are effected by the words of the Consecration alone, and not also by those which either precede or follow them." Abp. Lefebvre once gave the example of Cardinal Mindszenty who once said Holy Mass in Prison with little more than the Words of Consecration. Btw, Greek Orthodox wrongly believe Transubstantiation takes place during some of the prayers that precede the Consecration (some of those errors that had now begun to spread in Rome, and Archbishop Lefebvre was controverting that above) but this error of fact does not invalidate their Sacrament and Sacrifice when an Eastern Orthodox Divine Liturgy is celebrated. That's what the Church has ever held.
I've given you dogmatic reasons why the new rite cannot be invalid. You can choose to believe them or not just as you wish, it's up to you, Pax Vobis. If all Eastern Orthodox rites were in fact invalid (they are not), this would not affect the indefectibility of the Catholic Church. If the new rites are per se invalid (which Abp. Lefebvre, see above, said he would not so much as tolerate the Priests of the SSPX professing, as documented earlier), then the Church of Rome has no valid episcopal lineage, and no residential Bishop, which is heretical. It is dogmatically certain, then, a Truth closely connected to truths of faith, that the new rites cannot be per se invalid.
The Truth of God's existence will objectively be absolutely certain irrespective of whether agnostics doubt it or not. The Truth of Christ's Resurrection will objectively be absolutely certain irrespective of whether modernists doubt it or not. The Truth of the new rites minimal validity is also objectively certain, because of its necessary connection to Church dogmas like Apostolicity and Indefectibility, irrespective of whether explicit sedes or implicit sedes (people who don't realize they hold to premises that logically, but wrongly, lead to sedevacantism; that is, they need to revise their erroneous premise that led to a false conclusion) doubt it or not.