Indeed. And it's interesting that there was not a whisper of this in the original post in this thread. Anyone would think that BA had simply taken a last-minute full-fare cash booking.

Presumably, if AA had not managed to book (force a booking?) on the BA flight to reaccommodate the OP, the OP's entire party would have had an enforced overnight at LAX instead of being on their way. Did the OP apply any pressure to AA to do this? How did AA manage it on a flight that was already overbooked? Would the OP have preferred an overnight delay? The original post suggests perhaps not, given this part:-