Showdown on a checked river

[jalsing]

Robert's Rules clearly states that if everyone checks the river, the first to check is the first to show their cards. What isn't clear is what happens if another player shows first, what players are then REQUIRED to show their cards. Example.

At the river, two players remain, and first to act checks. A common sitiuation here is that the second player will infer a check, by saying something like "I just have pocket 4's" and flip them up. Player 1, having been on a draw or whatever (can't beat the 4's) mucks.

This same type of situation occured at a recent home game, and although I wasn't at the table, I was asked my opinion. Players at the table insisted on seeing player 1's cards, as he was first to act. In my opionion, by showing his cards first, player 2 forfeited his option to see player 1's cards (he could have waited for player 1 to show first as is the rule.) I think some of the players were under the assumption that player 2 earned a showing by actions on previous betting rounds (calling player 1's flop bet for example).

Any thoughts on the situation?