CathInfo.com

Billot seems to say that the universal recognition makes a de facto claimant a claimant de jure (see bold/underlined portion; legitimacy means legally, or de jure):

Finally, whatever you still think about the possibility or impossibility of the aforementioned hypothesis [of a Pope heretic], at least one point must be considered absolutely incontrovertible and placed firmly above any doubt whatever: the adhesion of the universal Church will be always, in itself, an infallible sign of the legitimacy of a determined Pontiff, and therefore also of the existence of all the conditions required for legitimacy itself. It is not necessary to look far for the proof of this, but we find it immediately in the promise and infallible providence of Christ: “The gates of hell shall not prevail against it”, and “Behold I shall be with you all days”. For the adhesion of the Church to a false Pontiff would be the same as its adhesion to a false rule of faith, seeing that the Pope is the living rule of faith which the Church must follow and which in fact she always follows, as will become even more clear by what we shall say later. God can permit that at times a vacancy in the Apostolic See be prolonged for a long time. He can also permit that doubt arise about the legitimacy of this or that election. He cannot however permit that the whole Church accept as Pontiff him who is not so truly and legitimately. Therefore, from the moment in which the Pope is accepted by the Church and united to her as the head to the body, it is no longer permitted to raise doubts about a possible vice of election or a possible lack of any condition whatsoever necessary for legitimacy. For the aforementioned adhesion of the Church heals in the root all fault in the election and proves infallibly the existence of all the required conditions. Let this be said in passing against those who, trying to justify certain attempts at schism made in the time of Alexander VI, allege that its promoter broadcast that he had most certain proofs, which he would reveal to a General Council, of the heresy of Alexander. Putting aside here other reasons with which one could easily be able to refute such an opinion, it is enough to remember this: it is certain that when Savonarola was writing his letters to the Princes, all of Christendom adhered to Alexander VI and obeyed him as the true Pontiff. For this very reason, Alexander VI was not a false Pope, but a legitimate one. Therefore he was not a heretic at least in that sense in which the fact of being a heretic takes away one’s membership in the Church and in consequence deprives one, by the very nature of things, of the pontifical power and of any other ordinary jurisdiction.”

I started this topic, but am now sorry that I did. Because it has become yet another religious cat fight among three or four CI forum members, who think that the majority of other members are vitally interested in their lengthy arguments and dogmatic certitudes. Are they? Really? I’m not sure what motivates these people.
Sean tries desperately to prove that V2 popes have been duly and fairly elected and accepted by the entire Episcopacy. Maybe so, maybe not.
Who knows what his underlying motives really are. After all, SJ just published a book with a written introduction by +Williamson. H.E. holds to the view that all these popes were legitimately appointed. It wouldn’t look good if even the mildest fragrance of Svism might waft up from its pages. +W and the R&R could not in conscience support any such content. So, one can at least speculate, Sean feels that he has to double down on his anti-Svism in deference to the bishop. He’s got real skin in the game.. But I’ll not spend too much time trying to second guess him. Why the others go at it so fiercely hammer and tong, they’ll have to answer for themselves.
Meanwhile, I repeat, ++Lefebvre was very close to going sede himself. I think that Francis would have finally pushed him over the edge, and into sede free fall.

Its just confusing to me because those same bishops accept Vatican II.  So why can they all be wrong on the one but not the other?