This is an excellent reason to have paper tickets, regardless of what the "Dr. Rick" insurance dork says.
AA usually defaults to their mileage plan and does not credit them to AS. What you have to do if this happens is have proof of trips taken (paper ticket) and relinquish the miles on AA.
As customer service can help here. You will need screen shots of tickets or AA travel proof (on website) and screenshot of the mile released page.