Here's why I considered folding.
Baysian-wize yes there is a higher distribution for QQ-99 (6ways for each vs 3 ways for AA or KK) because of card removal effects.
But most sane players don't 4 bet tight players (and I play tight usually) with anything but AA or KK or maybe AKs or QQ
Here JJ should just call or perhaps fold.
So I figured I'm probably facing AA or KK.
Especially from a loose passive.
Preflop? You're getting 12:1. Heck, you're getting the right price there to call even if he shows you 2 aces.
The fact that he may have KK-QQ or AK makes this even more trivial.
As far as expecting a LP to lay down "any" hand here, you are giving a bad player way too much credit. It doesn't matter what they "should" do, since they rarely will do what they "should" do. They aren't thinking anywhere close to the same level.
FWIW, I cap preflop, cap flop, call turn. and fold/call river.
River IMO is dependant on whether or not I've seen this player run any crazy bluffs. Is he running poorly? Typically a LP will have a hand here, but calling the river getting 17:1 isn't that horrible IMO (if you've seen him tilt or bluff especially).