Coach takes a charge!!!

[Damian]

You said it was a noisy gym and everyone including the coaches were into it. You did not say if both coaches entered the floor during their coaching.

I would think that if this had been going on for some time, calling a T at the end of the game would have been wrong. If on the other hand, you had buzzed the coach a few times and asked him to stay off the floor, then the T would have been given.