Airfare is not reimbursable. You may be able to make a small airfare transaction appear to be a reimbursable fee, but we have no reports specifically for AA.
Have we seen data points (AA or others) on incidental charges related to refundable tickets (e.g., prepaid baggage, seat selection), and the cardholder cancels the ticket? I wonder if the statement credit would get reversed when the incidental charge gets reversed.