AA is correct and BA is wrong. EU261 clearly states, that the operating carrier has to deal with IRROPS. No matter if your ticket is issued on AA or bought via an OTA, the operating airline which cancels the flight has to reaccomdate the passenger.
BA won't do it, because they'd have to pay for rebooking you on another flight so they go the easy way by saying you need to talk to the ticketing airline, which is incorrect.
AA also doesn't want to rebook you, because then they would need to pay for the rebooked flight even though they have not cancelled any flight.
BA is a massive PITA when their flights are booked on another ticket stock.
Iata resolution 735d is also clear on that, the airline which cancels the flight, has to take care of the pax and rebook him/her even on out of network airlines!
All that won't help much if they just deny it and won't do anything.
Best is to talk to the "oneworld Global Support" desks [MENTION=128682]LHR[/MENTION], they do not care which airline issued the eticket since they have plating authority over all OW members.

Usually if an airline denies your EU261 right to be rebooked on the next available flight (ofc that doesnt cover a voluntary change of origin), you'd buy a new ticket out of your own expense and sue the airline afterwards for reimbursement, thats what we do everytime and win in court.