So is it the fact that the OP tried to check in for the AA flight, and was told the flight was cancelled, and was then re-booked on BA?

If so, do you know for sure that AA was is a position to confirm you in J on BA (because that's what BA told them), or that AA was perhaps 'trying to get you off their hands by sending you to BA and hoping they would accommodate you'?

I guess the crux is the interraction you had (when, and with whom) that led you to believe you had a confirmed seat in J on BA