Speculations
I think one of the important pieces to this event is the time it took to go from FL370 to 15,000 feet.
I think I saw in some earlier post that radar showed this to be a rather short time. A shorter time that an emergency descent would take.
Maybe someone here can refresh that information.
I would think a cabin, avionics bay, or lav fire would allow time for some emergency call.
I know they may have been in a poor ATC communication area, but maybe another aircraft on the frequency would have heard them.