The AAdvantage Terms and Conditions are here, and include:

"On American Airlines and other AAdvantage airline participants, you'll receive AAdvantage mileage credit only for the class of service on which your fare is based when you are ticketed." This might indicate credit as per the originally ticketed fare (as on AA, not the upgraded class of service, but certainly the originally ticketed class of service. But in this instance, BA is the challenge.)

"Certain airline tickets are not eligible for earning mileage credit. These include, without limitation, the following: all tickets issued as AAdvantage awards or other free ticket promotions including free or reduced rate tickets; companion tickets; charter flight tickets; travel agency/industry reduced rate tickets; infant tickets; items occupying a purchased seat; unpublished fare tickets, including consolidator fares, tickets issued as a result of a fare published inadvertently or by mistake and tickets issued subject to special provisions." This would not seem to apply here. Again, it's BA that's the problem.

And unfortunately, yes, it can take months to unravel these issues - and require the occasional prod from the victim.