The Pilot must not comply with ATC demands/control/orders.
The buck stop with the Captain, he has ultimate authority over the operation of the aircraft whether in an emergency or normal operations.
ATC provides a service from the air-conditioned, dohnut and tea room bunker. If the crew believe a direction is not in the best interest of safety or operational procedures they have every right to fly the aircraft as they see fit......as the crew of this AA flight did.