In many hubs AA (probably a carry-over from LUS) have (re)booking centers--you don't have to deal with GAs to get rebooked.
I would think that if the GA off loaded you he/she would hold the power on whether to let you travel. Most reasonable GAs will simply allow you to simmer down and rebook you. But if they decide to bounce you all together you have zero recourse, other than apply for a refund.