Actually no.
My speakers have taken an early retirement so I haven't listened to the communications between American and JFK ATC so I'm not passing any judgement on this situation, speaking in general terms.
Sec. 91.3
Responsibility and authority of the pilot in command.
(a) The pilot in command of an aircraft is directly responsible for, and is the final authority as to, the operation of that aircraft.
(b) In an in-flight emergency requiring immediate action, the pilot in command may deviate from any rule of this part to the extent required to meet that emergency.
(c) Each pilot in command who deviates from a rule under paragraph (b) of this section shall, upon the request of the Administrator, send a written report of that deviation to the Administrator.
The above is FAR 91.3. It is the regulation I fly under. I would be very surprised if in your country pilots aren't given the same latitude.
The regulations are very clear, I'm provided the latitude to do I as I need to keep the aircraft safe. I may have to answer and receive judgement from others on the ground but I don't need squat from the controller at the moment if the situation is that dire. I don't know if it's an ego thing for the controllers, but that's just the way it is. If time permits I fully acknowledge that working with the controller is in the best interests of all involved and that almost all emergencies allow time to receive "amended clearances", but somewhere someday there's going to be a situation in which the PIC must make an immediate decision.
Yeah, just what I want to do, wait on a congested frequency not able to get a word in, or dealing with a controller who may not fully grasp the magnitude of the emergency, a controller who denies something because of a perceived conflict with traffic, etc, etc as I wait for my "amended" clearance.
I'll amend my own clearance if it's dire enough thank you very much.
You can retort all you want, it won't change the authority I have to do as I need to. Might make you feel better, but that's it.