I would print out a copy of your AA.com account that reflects the mileage awarded from the flight, as well as the date. That is pretty solid proof that you put your butt in the seat on that flight.
(In the future, you might want to do what many of us do and OLCI then print the boarding passes to PDF and email to yourself. That way, you always have a record. I also save my printed boarding passes for posterity in a cabinet, but that's just my personal quirk.)