You yourself said that to be consistent with his implicit faith form of BOD, +ABL should've accepted Vatican 2 since he was already adopting EENS-denying ecclesiology. And he's far from alone, pretty much all the Trad clergy agree with him. So by your own words, they should all accept Vatican 2 to be logically consistent with their beliefs.
As I understand him, Lad is only talking about accepting V2 for this one particular point. Obviously, the other 2 major heresies of V2 (there are a multitude of minor ones) - religious freedom and new-world ecuмenism - are separate issues and most Trads don’t accept these.
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One could argue that these 2 errors flow from the liberal-BOD view, but most Trads don’t go all the way over the heretical waterfall, even though their liberal-BOD canoe brings them close.