I agree with your point that MX didn't handle it well, in that, there should have been instruction in place for AA agents there to rebook you, or what the pax should do.

In terms of where the MX agent/manager went, it sounds like he was off to take care of departure Ops responsibilities so it would be unlikely he would be back until after the plane had left. Again, bad communication. Also, if you ended up on UA, lost revenue for MX.

That said flying without status on any airline, it pays to leave plenty of time as I have seen many snaking Y check-in lines for AA at JFK, LAX, MIA, ORD, etc.

PS - Write a complaint to MX and state that there were approximately 40 people who were not checked in. If what you say the AA agents claimed, that it is a zoo inferring that this happens regularly, perhaps MX management might take notice if there is an exceptionally high factor of having pax be denied boarding.