I didn't mean that online reads are useless, not at all. In fact, I rely heavily on them to make certain plays. What I mean, and perhaps I could have been clearer on this, is that the person who responds to the OP usually only has one hand
to judge what a player has, and that's
when presuming it's a set (or some other monster) is ludicrous.
The example you give about the PPT is somewhat analogous to my Dan Harrington example; it's possible that he had a very good read on the player, but he also knew that he was playing a solid opponent. It's a mistake of abysmal proportions to presume that a similar bet in a low limit online game would be anywhere near as likely to represent a strong hand.
As a sidenote, I'd be very very cautious, even with an extremely solid read on a low limit player, to think that a set is the most likely holding. And in limit, I don't think I'd ever lay down two pair on the suspicion that my opponent has a set. The likelyhood of him having a set is virtually always small in comparison to the pot odds
Edit: I perhaps didn't actually answer your question, MrS, sorry about that. Let me qualify a bit more.
If I have a read on a person that he donks the flop with top pair, but checkraises the turn with trips, how often am I willing to fold the turn with an unimproved AA? I only have solid enough reads like this on limit players at this point, so my answer goes for limit: Not often. I will fold weaker hands (second pair, etc.) if it happens, but if the board is Q-T-5-2 and I bet the turn with AA and get checkraised, I'm not likely to fold, even if I know that he will often have me badly beat. And I don't consider it a leak in my game. Let me explain why:
1. My read is often going to be wrong. People don't get trips very often, and the fact that he checkraised me twice with trips is not conclusive evidence that he does it everytime with trips, nor that he only does it with trips-or-better.
2. Everyone bluffs. Not everyone checkraise bluffs (I have a favourite opponent on Stars that never* does, which is kinda cool to know), but there's still some probability that this is the case.
3. You usually can't really tell the difference between a two-pair-hand and a set. Someone who limped in with T2s is as likely to checkraise this turn as someone who flopped a set (if not more, since there's some portion of the time that a flopped set will checkraise the flop). And against two pairs, I have outs, and virtually always enough outs to make a checkraised turn profitable to call (with AA, there will be at least two bets in preflop, one on the flop for each player, so if it's heads-up, the pot is 3 big bets on the turn, then I bet and get raised, so now it's 6 big bets and one back to me. Against any two pair hand, I have 8 outs, so I can't fold).
Reads are important, and they should be used to narrowing hand ranges. But the overwhelming amount of evidence needed to support a theory that states that someone's hand is most likely to be a set (when no flushes or straights are possible) is virtually impossible to reach online. Pot odds
very often makes up for the uncertainty in hand reading, so folding two pair is very often a mistake in a situation like that. IMO.
* This read is probably not foolproof either, but it's pretty damn close. I have about 1000 hands on this person, and it hasn't failed me yet.