(reawakening an old thread)
This just happened to me.
Bought tickets on Finnair stock, all segments flown on BA, all segments' boarding passes showing AA FF#.
AA doesn't even have a record that I flew half of the segments; the other half show as zero credit.
I claimed it from AA, a month later AA answered only about two of the four, saying denied due to miles having been credited to BA FF program.
Only problem is, I don't even have a BA FF program membership. Logging in to BA's website and clicking the Executive Club link shows me an offer to join, NOT an account. (I knew this). (For completeness, I also checked via Avios, and via the one other associated airline on which I once upon a long time ago collected a few points - Vueling. All nonexistent or zero balance, as expected). (Oh, I also verified that I don't have any trip history nor transaction balance with Finnair).
Incompetence is so frustrating. I just submitted a complaint to BA asking them to cleat this up (though, why should they care about me, since only my body was their customer, but not my FF soul, obviously?) and followed up to AA (who clearly don't care much either, since they'd already seen my boarding passes with AA numbers on them). *grr*
Working on it...