I was quite imprecise here. What I actually meant was that there was no way to change to the AAdvantage number after a booking is made (at least when last I tried). I made a couple of BA vacations bookings (even cheaper than regular BA bookings for the same flights) and they were somewhat complex with the Avios things I wanted to do, so I didn't add to it by throwing in the AAdvantage number during booking, so it got BA number. Then there was no way to change it on BA.com, so I went to rj.com.

I don't actually recall if I've done a straight BA booking on BA.com, so didn't know whether this allowed choice of frequent flyer number at booking. Seems that it does.

Sorry for the prior incomplete response and thanks for the correction.

Cheers.