You have found one of the biggest scams the AA runs. On aa.com, there is no way to force a fully-refundable fare, only this “Flexible” fare. aa.com also makes it near impossible to find the full fare rules (and then you must look for the word “refundable;” else the assumption is that it is non refundable).
Telephone agents are not much better. I have booked refundable fares over the phone, only to see a non refundable endorsement on my ticket receipt (and not the receipt they send, but the full, detailed receipt on aa.com). I’ve even had agents insist the fare is refundable, and they then see the non-refundable endorsement after ticketing. Lately, I’ve heard “We do not sell non refundable fares in that market.” Huh?
Best advice from an AA ExPlat for several years: Book with another carrier if you need a refundable fare.