Lad says right here "if you don't at least have a positive doubt, then you have no business being a Traditional Catholic, for you are a schismatic".
Lad can correct me, but after reading hundreds of his posts (as you have done too), I interpret his theory as saying that:
1) a Traditional catholic, by definition, does have some doubt/confusion about the V2 popes, because they attend a non-rome sanctioned mass.
2) A traditional catholic, by definition, receives sacraments from "schismatic" (new-rome's perspective) priests.
3) A traditional catholic implicitly rejects V2 and new-rome's authority (in favor of Quo Primum's authority) by attendance at non-rome sanctioned Trad masses, just as anyone who attends an indult implicitly accepts V2 and the new mass.
4) Xavier is an example of Ladislaus' hypocritical schismatic fake-trad, because he fully believes that the V2 popes are popes, and yet he attends Trad masses. He ignores canon law and goes wherever he wants.
All Trads are implicit V2 pope doubters. Sedes are just explicit about the doubt and take it to the extreme. ...Even most conservative novus ordo-ites are papal doubters. It's a sign of the times - confusion.
He considers those who understand that the pope is the pope to be in schism - yes, he is confused.
That's an over-simplification.