It would appear to me that the R could invoke 2-5-5:
"The referee shall ... Decide matters upon which the timer and scorer disagree and correct obvious timing errors."
That rule doesn't state whose error can be corrected, only that the R can correct obvious timing errors which we definitely have. Since the foul was after the buzzer, I would probably put 1.94 seconds back on the clock and start from there since we couldn't be sure if the foul would have occured before or after the clock *should* have expired. Just my .02.
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