Since I started following this thread years ago, I remember two cases - perhaps there are a handful more over all of the years of FlyerTalk - where AA had a false positive. In both of those two cases, the original posters were made whole. JonNYC was able to provide a little more insight when I had mentioned this awhile ago.
In one case, I don't think we ever got the full story, but I remember it involved a poster trying to get back to the US from South America. In another case, a fellow poster had his account accessed without permission. He proactively contacted AA but was subsequently put in lockdown mode by corp security. In both cases, the affected members maintained their composure, cooperated fully, and provided what details they could. I believe both of these cases were resolved within a few days.
In OP's case here, even if there was no wrongdoing, the optics of the situation are poor from the perspective of a third party observer. OP's responses to the requested information did not help the situation based on the outcome. AA is holding the cards in these cases, and the burden of proof falls on the member.