BA's No Fly List takes some (mainly physical) effort to get on it, and not much effort to get off it. But yes, while being overbooked is a possibility, I think it's probably a rabbit hole that isn't necessarily correct. For example if the AA flight component was changed, the ticket may have needed reissue or revalidation, which should have been done by the TA, and most TA's (as opposed to online booking companies) are very much on top of that.. If the ticket is reissued/revalidated at a late stage then there may be no seats left, or other difficulties at the airport. As ever, it's important to check the ticket number in the App if OLCI doesn't work, see the main thread on OLCI failtures for more information.