The gate deadline for international is T-30. Doors close at T-10. But, that has nothing to do with whether your friend was at the gate at the required time. If he blew that deadline, he is SOL and properly offloaded. No EC 261/2004 (EUR 600) or DOT (400% of segment fare to a maximum of $1,350) compensationThat leaves the question of whether your friend was at the gate by T-30. He apparently has told you 09:31 and AA says it was after 9:35. That is a factual dispute.
AA's system will have logged, to the second, when your friend was off-loaded. So, that is going to be hard to beat.
Once the gate deadline has passed, any standbys processed, the flight will be closed and depart because there is no particular reason to wait around. Thus, unimportant that the push was early.