When you check behind on the flop, aren't you basically typing "I don't have a good Ace and I'm scared of being check-raised" into the chatbox? Doesn't that just give villain license to lead the turn, at which point you still have no idea where you stand? I'm with the Addict, I think I'd rather fold to a check-raise and be done with the hand then get deeper into the hand without knowing where I stand. Hero got a bit lucky that villain threw out such a small turn bet, but what if villain leads the turn for 1/2 pot there (as played)? Or bets small on the turn and then fires out 4000-ish on the river?
if villain leads for 1/2 pot on the turn, then by calling that bet we'd already be at the river compared to still being clueless on a drawy A-high flop after being check-raised and while having invested the exact same amount.
so folding to a large river bet doesnt cost us more than folding to a check-raise.
sure, he might have hit his 2-to-5-outer on the turn, but the overall spot we are in is much better than facing a check-raise i believe.