Situation in NLHE tournament: One player was betting on heads up river and got called. He mucked his hand and said "The pot is yours." Does the second player have to show his hand to claim the pot?
No the second player does not have to show his hand. If a muck is allowed than he does not have to show.
This should again be written in the "house rules". In some Casinos every hand has to be shown at a paid river. Last action shows first. Calling is not an action. So the guy who bets / raises lasts should show first.
But if he is allowed to muck his hand, why shouldn't apply the same rule for you after taking the pot? ;)
I don't think you would have to show your hand in this situation.
Not sure why anyone would muck their hand without seeing what their opponent had though. Even if you were playing something stupid, you could still have a better hand than that of your opponent.