In what situation would pressing the "off" button on a GPS transmitter that is currently on fire achieve anything? I think in general, a GPS transmitter will do a pretty job of turning off all by itself when its components are on fire. The likelihood of an electrical signal to an electrical device that is currently on fire doing anything at all is very slim, including when that signal is "turn off".
There are already plenty of components on an aircraft that cannot be turned off by the pilot while in flight. The black box being the blindingly obvious example. They have transmitters that the pilot cannot turn off too, which is where the information in the article comes from. I have read that Malaysian airlines weren't using the transmitter to transmit more detailed information simply because they had not paid the subscription to use this advanced tracking. It seems like it would be helpful if such tracking systems automatically monitored the location of aircraft even if they don't do advanced performance monitoring purely to assist with emergency search and rescue.