Scoring error

[filinuk]

At the end of overtime, the official scorer notices that the home team scored one additional point in the 4th quarter before the officials leave the court and verify the final score (Visitor 62, Home 61).

The referee rules that once overtime begins, there can be no corrections to the previous quarter. Is this correct?

I agree that the home team can't be declared the winner in regulation once overtime starts, but if the error is spotted before the final score is recognized, can't the official add the point and play a second overtime if he feels the error is justifed?

Thanks.