Downgrade is reimbursement rather than compensation, so BA treats it as a transaction against the original ticket, as if it was a part refund. When BA holds the ticket and does the downgrade then it's in theory easy enough for BA to process. But if AA issued the ticket, the refund - in BA's eyes - comes off AA, even though BA is sitting on the AUP funds. So BA would in that specific instance invite the OP to go to AA for the refund. Legally BA remains responsible. Compensation and right to care are treated differently, so you seem to have been correctly advised. Some people get processed in 2 weeks but you need to submit a 2 sentence complaint for that to happen.