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2-2-4 says, "THE final score." There is no final score unless the game has ended (or could end), and the game doesn't ever end in a tie. There's no question that if there is an error in the book that has one team with more points at the end AND the officials leave the confines of the floor the game is over. However, if there is NO error in the book and it indicates the score is tied, the game is not over regardless of what the officials have done. There's no provision for a tied game, unless its declared interrupted or suspended.
So, assuming you have a score book that is correct (tied in points) and a scoreBOARD that is not correct (one team has more), when its pointed out to the officials, the game CAN continue without violating either the provisions of 2-4-4 or the casebook interpretation -- based on the scoring and overtime rules in Rule 5. I don't see anything in the rules that:
1) defines "final" or "final score." Thus, based on Rule 5, you have a tie game which means OT;
2) makes the scoreBOARD score official and the score that the game is left with if the officials leave the court;
3) specifically defines the word, "score," which means we look to the rest of Rule 2, and it is clear that it is the BOOK that determines what the real score is, not the scoreBOARD.
We leave the confines of the playing area at halftime, but the final score is not approved then. 2-2-4 doesn't specifically state at the end of the 4th quarter or at the end of an OT. Thus, it HAS to mean when a final score COULD POSSIBLE be approved, and it can't possibly be approved in the case of a tie.
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