I don't know what's happened to PPRuNe lately but there appears to be a flight simmers takeover. Along with some very ill informed rubbish spouted from people who should know better.
There isn't a jet flying that was certified in the last 30 years that doesn't demand a shutdown for an engine fire warning. No matter how brief the warning was. There is some variation as to whether the extinguisher is fired after the engine is isolated but in most cases it is.
It would take a very brave(foolish) man to keep an engine running for no better reason than the warning went out.
Here is a summary of a few QRH:
BBJ/73 classic/73 NG - shut it down and if the fire switch light or ENG OVERHEAT light stays illuminated use the extinguisher
Avro RJ (aerobat77 take note) - shut it down and fire the extinguisher.
Embraer 145 and Ejet - Shut it down and fire the extinguisher.
l1011 shut it down and fire the extinguisher.
A330 (RR) shut it down and fire the extinguisher.
Get the picture?