Semi-correct:

1) they would have been booked on the same route 2 months later in AA F (even though on a J ticket), which is what triggered the 210 TPs

2) booking via BA does not mean that the flights have to be booked on the codeshare. BA (over the phone) can book the prime AA flight number, which would also be booked in F, and therefore not having any influence on the TPs.