What's the rule, what's the call, what's common sense?

[rainmaker]

The thread below about a foul at the end of the game called this situation to mind.

Hypothetical Question:

The rule book says that "No free throw(s) shall be attempted after time has expired for the fourth quarter or any extra period, unless the point(s) would affect the outcome ofthe game."

So here's the sitch: Last game of the season, team not advancing to play-offs. Team A down by two, A1 (who is a senior) shoots, ball released before the horn, A1 is fouled. A1 misses the first FT. But the coach had come to you before the first FT and said, "A1 only needs one more point to break our school's career scoring record. Can he shoot both shots regardless?" What do you do?