Unfortunately, in many cases it is a 'damned if you do, damned if you don't' scenario for the subsequent inquiry, and has led to much crew room discussion.
'Check for signs of fire': great in most circumstances, but remember the sensors are (generally) around the engine bay and it could be something else. A hot gas leak - should go out at low power so may be a good indicator, but is it doing any other damage?
Like Fareastdriver I too know what a real turbine fire looks (and sounds) like, but not the insiduous problems, although I have also seen the results. Spurious warnings are much more common, particularly in wet conditions, but I've only had two real fires on rotary - one was indicated but accompanied by a loud bang and associated indications; the other was a call from the back - 'hey capt, did you know the port engine's burning?'. Both times I was also well placed for a land immediately situation, but for a few of the spurious ones I was IMC and took the other line with 'no other signs'. It doesn't half concentrate the sphincter though.