This ruling can't be right, can it??

[renodoc]

I don't want to get too much into the details of the hand, just want to know if the ruling at the end is correct. I have 62s and raise preflop in a 1-2 NL game and get 3 callers.

Flop comes A-4-2, with one of my suit. BB checks, I check, player directly to my left bets, BB calls, I call.

Turn gives me a flush draw. BB checks, I check, player bets, BB folds, I call.

River misses me-- we both check.

I have no desire to show this piece of crap pair of deuces that I'm holding, but there is a small chance that the villain was on a flush draw also and I'm good. My interpretation of the rule is that since villain initiated the last bet (on the turn) and was called, that he is obligated to show his hand first. The floor told me that "a check is action" and since I checked on the river, I initiated the last action and I had to show first. This makes no sense to me as basically, unless there is a raise on the river, the player who is out of position would have to show first everytime. amirite?