The likely alternative to the AA miles (which are helpful if you are doing non Reward Flight Saver flights outside of (mainly) Europe) is a voucher for a US dollar amount of spend on an AA booking. Though this can be used on many BA services, nevertheless this has done via AA, is slightly fiddly to book, and the likely context is a US based itinerary. I doubt the cash amount would be that high but searching the AA forum may give you a hint about that.

As this is a customer service gesture, I too would open up an account just to churn the miles.