CathInfo.com

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:
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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.
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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.
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He considers those who understand that the pope is the pope to be in schism - yes, he is confused.

That's an over-simplification.  

That's an over-simplification.  

It's either deliberate oversimplification or else he can't think straight.  Actually, I think it's a blend of the two.  Due to confirmation bias, he filters out distinctions that don't fit in with his preconceived conclusions.