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I believe that this is not a correctable error.
I contend that by "Erroneously counting or canceling a score" the NFHS does not have this type of play in mind.
Rather the NFHS has this in the book for failure to award points due to BI or goaltending, getting the value (2 or 3) of a shot correct, and judging last second shots at the end of quarters/extra periods.
In my opinion the FAILURE TO RECOGNIZE A VIOLATION is all that happened here and that is not a correctable error.
The failure to call the violation for the ball passing over the rectangular backboard only resulted in not awarding possession OOB to the opponents. It did not directly result in the score. The fact that the ball actually went through the goal is responsible for that. By that I mean the ball could well have passed over the backboard and not gone into the basket. The two items are not necessarily connected.
The bottom line is that since the violation was not recognized, the ball remained live and subsequently passed through the basket. Although the ball does become dead when a violation occurs, not when the whistle blows, that assumes that the violation is actually recognized and called on the play.
So, according to 5-1-1 we have a successful goal that should count. Therefore, the score was correctly counted according to the rules.
For a test case let's replace that violation with a different one. A1 is driving to the basket and travels. The officials fail to recognize the violation. A1 shoots and scores. There is no one on this forum who would argue that the officials could stop the game at the next dead ball and cancel the basket. That is absurd.
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