I find myself checking behind the turn *a lot* at 400NL. After a PFR + a called cbet you're either up against
- a draw
- a hand which is way behind (a PP who puts you on missed overs, e.g. J33 flops).
- or a hand which is way ahead (set/2 pair; limpcall EP/MP from a nit.. watch out).

If it's unlikely Villain is drawing, checking the turn behind is the right move.

Anyway, in this hand you're pwned by a full house I think. He pushes the river to make it look like a busted draw.