Please Help! Do I have to show my mucked cards?

Do I have to show my mucked cards?
I was playing in my home poker tourney when this situation occured:

4 players, A, B, C and D were in the pot when player A, acting first bet out after the flop.

Action folded to D who called. Both players checked on the turn.

On the river, A bet and D called. After which, A mucked his cards (declaring D the winner) not wanting the others to know what he had bluffed with.

A slight disagreement broke out from the players who wanted to know A's cards, claiming since he bet first, he should reveal his cards. Whereas A argued that he need not show his cards since he 'surrendered' this game and mucked his cards.

This differs slightly from the all-in scenario. Who is in the right?

Someone bet and someone called on the river. The bettor shows first and then it goes around clockwise for each person who called.

Hope that helps, good luck!

If D had called and then flipped up his hand first in excitement, A could have mucked. But A needs to show.

The way I understand it the bettor is supposed to show first. I have seen a game on TV (WPT I think) where player A bet and then mucked as soon as player D called. Honestly if that type of thing happens then you really dont need to see player A's cards do you? You should already know its a stone cold bluff.

Even if D would have bet and A called, if they wanted to see your mucked cards they have the right to, although it is considered very impolite to ask. That is why you can see mucked cards on the HH on online poker.

Played D paid to see Player A's hand so Player D has the right to see Player A's hand.