Very good, but have a hard-copy printout available to show AA, and be aware that you might get some pushback. Escalate to a supervisor, if necessary. If you are forced to pay to check a bag, be sure to get a receipt for the payment if you think that you might want to seek reimbursement from AA or IB -- perhaps with the assistance of the U.S. DOT -- down the road.

Good luck, and please let us know how it goes.