Maybe in the future as you're running by the AA ticket counter to get through security, let the AA staff know of your presence and ask them to call to the gate to let the gate agent know you're on your way (and why you're running).

Coming from a different airline, the GA may not have known you were connecting and thought you just weren't showing up. A call from the front desk a few minutes before you get to the gate may have been all that was needed to save your seats. (Having been to Detroit a few times, I know the AA counter is pretty close to the security checkpoint.)

The situation isn't good by any means, but sometimes a call from another AA employee to a GA explaining the situation works and kinda sorta slows the clock down.