Classic problem of one person looking at things in odds form and the other looking at things as a percentage.

Both PokerPatNEU and underminedsk are correct (except for the parts where underminedsk says Pat is wrong).
With $10 in the pot pre-flop, a $10 post flop bet will give the opponent 2:1 odds, he would need a 33% chance to win to call.
He's putting in one to get 2 (hence 2:1 odds), and he needs to win at least 10/(10+10+10) = 1/3 of the time.