I would be very much against any blanket rule that says a hand is still live until it hits the muck. I don't think there is one, and I don't think there should be one. I think that this would just invite angle-shooting, and I've seen it happen.
In my view, if you throw your cards in towards the muck in a folding action, then your intention is clearly to muck, and players should be held to their intentions once physicalized as the general rule. If the Rules were to permit players to take cards back so long as the cards haven't hit the muck, and the Rules were to explicitly provide that the hand would still be live in those cases, what would stop people from throwing their cards forward in a folding motion, and then taking them back just before the dealer can bring them in, hoping that in the interim, the next player(s) might have given some indication that they intended to fold?
Yes, all problems would be solved if dealers mucked folded cards right away, but let's be practical, there will always be some delay, especially if a player purposely throws the cards in a spot out of the dealer's immediate reach. Dealers are human beings, not machines which can instantaneously react to the depression of a "Fold" button in a user interface.
Consider players A, B & C. If A is first to act, and B is considering calling but is worried about the player behind him (C) calling or raising, this would be a perfect opportunity for B to see how C might react to a "fake" folding action. In my mind, being permitted to throw ones cards in and then retrieve them before they are mucked ("Oops I changed my mind", "Oh wait, let me think some more about this"), is no more legal than a string bet would be... In fact, I would call this behaviour a "string fold" and it should not be permitted.
I can appreciate that there will be times where there is misinformation which was relied upon by a player, and if it was not for that misinformation, the player would not have folded. For example, it is showdown, all action is complete, and one player has lied about the contents of his/her hand. OK, the TD can consider the circumstances of that case, and rule that another player should be able to retrieve the cards where possible out of fairness in extreme cases, perhaps under Rule 1. But that should certainly be the exception, not the Rule. In general, if a player's actions show a clear intention to fold, or to perform any other action for that matter, you should be held by that intention except in the rare circumstance where it would clearly be unfair.
The short answer, even though there were many errors made by the dealer, the hand is still live until it hits the muck.
Nick, I am surprised by your stance on this, considering your earlier post where you use your chess move analogy. Clearly the SB in that example threw his chips into the muck. Piece moved, period. There is nothing that would suggest that he erroneously folded based on misinformation. Why should the hand be live, dealer error or not?
And I must respectfully disagree with the position that the dealer should not have counted UTG's chips. It is the SB's turn and he is entitled to a count of UTG's wager. The dealer should have no discretion in this matter. While it may be obvious that the UTG had
him covered, it is not up to us to judge why he wants a count, especially since the SB is not the last to act. Perhaps he knew the size of the BB's remaining stack but not UTG's, and wanted to know whether UTG's bet was large enough that BB would seriously consider folding or not. Who knows. And if the dealer didn't notice the SB folding mid-count, then he didn't notice it. He's looking in the other direction, after all. But when he does notice the SB's cards on the table and then sees him picks it up, the hand should already be dead.