OK, so it is after all betting action is complete and therefore is not a non-standard fold. However, if Player A mucks at showdown wouldn't it be considered soft play? After all, even deuce trey off could split the pot.
Interesting discussion... not arguing the merits one way or the other, we just need to make sure it's clear what the 2015 rules say (and don't say):
1: This is a non all-in showdown. Players are not required to show their hands. They may choose to discard face down.
2: If cards are not spontaneously tabled or discarded, if there's betting on the river the last aggressor must show first (or discard). If no river betting, whoever would be first to act if it were a betting round must show first.
3: If there is betting action on the river, anyone who "pays to see the cards of the final aggressor" has a guaranteed right to see those cards on request. Any other request to see a hand is at TDs discretion, is not guaranteed and may be allowed or denied. No request to see a hand (guaranteed or not) will be honored if the player does not retain his cards or has discarded his own hand without tabling. This is to encourage players to show their hand and was adopted in 2011 if memory serves.
4: The question of whether a hand shown by request is live or not has not been fully established. Some houses consider all cards at showdown live, no matter the circumstances, while others consider a discarded hand shown at the request of other than the presumed winner to be dead. I think nearly every house considers a hand shown at the request of the presumed winner to be live. This was discussed in 2013 but a supermajority was not obtained at the Summit itself. Good topic for 2017.
To Bills question of whether a bet-muck is considered soft play, IMO not necessarily. More often than not it's probably a bluff bet that a caller picked off and the last aggressor would prefer not to show his bluff (or what he thinks is a loser).