No right of carriage
AA nor any other carrier is obligated to fly anybody. By buying a ticket, the carrier and the PAX are entering a contract. As any contract, this one is subject to condition which must be meet by both parties. One of those conditions is that a PAX may be of no threat to the operation of the flight. From being ever so slightly unruly al the way to terrorist intentions.
If AA had such suspicions then AA should have denied the flight to Mr. Ried on basis of a breached contract – they could even have kept the airfare!