[Nevadaref]

Here's what I found:

[A]
OFFICIALS PROVIDE ERRONEOUS INFORMATION
8.6.1 SITUATION: A1 is about to attempt the first of a one-and-one free-throw situation. The administering official steps in and erroneously informs players that two shots will be taken. A1's first attempt is unsuccessful. The missed shot is rebounded by: (a) B1, with all other players motionless in anticipation of another throw; (b) A2, with all other players motionless in anticipation of another throw; or (c) B2, with several players from both teams attempting to secure the rebound. The officials recognize their error at this point. RULING: In (a) and (b), the official's error clearly put one team at a disadvantage (players stood motionless and didn't attempt to rebound). Play should be whistled dead immediately and resumed using the alternating-possession procedure. In (c), both teams made an attempt to rebound despite the official's error and had an equal opportunity to gain possession of the rebound. Play should continue.

In this case, despite the official desiring the ball to become dead, it did not. In two instances, it NEEDS to be WHISTLED dead. In the third, the action of both teams overrides the official's statement and the ball should remain live and play should continue.
Conclusion here, the de facto action of the game takes precedence.

[Counter argument: (since I am seeking the truth, not just trying to make a case against what BITS wrote) The official who was overridden by game action in this play committed an error. The Trail official in the play under debate did not do anything erroneous. He intended for time to continue to be out and the ball to remain dead. It is unclear if his partner did something erroneous.]


[b]2.10.1 SITUATION B: A1 has been awarded two free throws. Erroneously, the ball is allowed to remain in play after A1 misses on the first attempt. A2 rebounds the miss and tosses the ball through the basket. B1 secures the ball and inbounds it. Play continues until a foul is called on A2 as B is passing the ball in B's frontcourt. RULING: The goal by A2 counts, but the error of not awarding A1 a second free throw is no longer correctable. Since the ball remained in play on the missed free throw, the clock started and the ball became dead when the goal was scored. When the ball became live on the subsequent throw-in, the time period for correction had expired.


Here is a very instructive play for our purposes. In red, the ball is erroneously made live. That seems to be what happened in the play under discussion. In blue, game action occurs with this "live" ball. Someone scores a goal, someone makes a throw-in, someone commits a foul. The ruling in green tells us that the game action counts! The goal counts. This game action is not nullified.
However, it isn't perfect for our discussion because I would like to see a definitive ruling on what happens if the play is whistled dead after the goal is scored by an official who realizes that an error has occurred. Can that goal be nullified? I don't believe so, but I'm not the NFHS authority.
Also, the play doesn't tell us if the Trail/Center chopped in the clock. That seems to be the case because the clock started, but what if it isn't the case. What if the T/C signalled continued time-out while A2 rebounded the miss and made a basket, then he blew his whistle? Was the ball ever live? Was the goal scored with a live ball or a dead ball? Does it count now? Does the whistle have to be sounded prior to the release of the try for the goal to be cancelled? I just don't know. Chuck, this should go on the list. Expand this play so that it contains these different variations.


[C]
A SPECIFIC UNSPORTING ACT
10.1.8 SITUATION: Immediately following a goal or free throw by Team A, A1 inbounds the ball to A2 and A2 subsequently throws the ball through A's basket. RULING: The following procedure has been adopted to handle this specific situation if it is recognized before the opponents gain control or before the next throw-in begins: (a) charge Team A with a technical foul; (b) cancel the field goal; (c) cancel any common foul(s) committed and any nonflagrant foul against A2 in the act of shooting; and (d) put “consumed” time back on the clock. COMMENT: If there is no doubt the throw-in was a result of confusion, the entire procedure would be followed except no technical foul would be charged. This procedure shall not be used in any other throw-in situation in which a mistake allows the wrong team to inbound the ball.

Game action which is erroneous takes place because Team A shouldn't be making the ball live, when the error must be recognized in order to do anything about it, and subsequent nullification of that game action and the time is even reset.
Of note here is that all can be fixed prior to the beginning of the next throw-in. The Trail came and told the Lead prior to that next throw-in in the OP's play. The officials erroneously allowed the ball to become live and a goal was scored, but in this case all of that can be wiped out. So did the ball actually become live here? Is this play revelant to our discussion? It does involve a team doing something unsporting or by confusion. The OP's play does not. Also, the NFHS was very careful to limit the scope of this ruling to this one specific act. This procedure shall not be used in any other throw-in situation.


Conclusion: To me plays A and B carry more weight than C because of its narrrowly construed context. Game action seems to be more important than what the officials mistakenly say or do. The game action which took place should stand. That seems to be the most correct by the rules as well as the most fair decision.