Rather than speculating about the GA's misconduct, if you believe that you have been done wrong, send in a complaint form.
Make it 2-3 short declarative sentences and leave out all of the irrelevant stuff. All that is important here is that AA requires passengers to be at the gate by T-30 for international departures and that you were, but you were told by a GA that this was too late as your name had been called sometime befo
If I were you, I would stick to the facts you know. AA can see exactly who cleared, how they cleared (instrument), and when.
The policy answer is that AA ought to specifically state that UG's must be at the gate no later than T-45, but the practical answer is that this is the case.