Correctable Error or Bookkeeping Mistake?

[tazzeroo2002]

I've been studying the correctable error aspects of the rule book recently, and had a situation in a game recently that got me thinking. Consider the following hypothetical situation.

Final seconds of a tied game and a held-ball is called. Officials look to the table and the scoreboard, and both indicate possession belongs to Team B. Officials award Team B a AP throw-in. Team B runs a last second play and scores a goal and the final horn sounds. After the final horn, and before the officials leave the court, Team A's coach asks the official to check with the official scorer about whether the arrow was set incorrectly. When you discuss the situation with the scorer, it is discovered the scorer has a record of the running AP. The book indicates that Team A should have been entitled to the previous AP throw in.

I realize that awarding the wrong team the ball for an AP throw-in is not a correctable error. However, could the actual wrong setting of the AP arrow qualify as a "bookkeeping error", and thus be corrected anytime? If so, how would you correct?

I'm guessing there isn't anything you can really do if you follow the letter of the rule, but I'm curious how others might view this.