Christine: I'll offer a slight twist to this subject... First, the bottom line... whether a called hand must be shown at showdown is at this point a house-specific rule. The TDA does not have a requirement that a called hand must be shown at showdown... Now to walk through some of the specifics:
1) The condition you describe in your original post is a "bet-muck", where Player A bets on the river, is called, and then mucks at showdown...
2) At the 2009 TDA Summit, there was an extensive discussion on this topic during the 2nd day, because alot of members wanted clarification on how it should be handled if a player elects to muck face down at showdown.... Where that discussion was left was that it is appropriate for the dealer to respect the muck of ANY player at showdown, and formally kill the hand by putting it to the muck. Keep in mind that the mere verbal declare 'I fold" (or any other verbal utterance) does not kill a hand because the word "fold" has no meaning at showdown, because we're not parsing words at showdown, we're reading cards and letting them speak. As long as the cards have not been killed by the dealer they can be tabled by the player and are live...
3) Once the dealer has taken possession of the hand and moved it to the muck it is now killed. HOWEVER the "winning" player can still ask to see the hand. If he so requests THE HAND IS LIVE and can win the hand if it beats the "winning" players hand.
4) The remaining issue is whether the hand must still be shown if the "winning" player doesn't request to see it (because it was a called hand), and this is a house-specific rule that varies by venue. Perhaps some additional progress can be made at formalizing a TDA position on this at the next Summit. Thanks alot for your question!
Thanks to Dave Lamb for clarifying these details... Also, here's a link to an extensive thread on a similar question that may be of interest to you:
http://www.pokertda.com/forum/index.php?topic=156.0