F43 - I think its my memory that is jaded. I wasn't in the company at the time and I suspect your version is the correct one, though of course the message that its a very bad idea to be flying on the engine that is on fire, with the other one at idle/shut down, is unchanged.
One thing which can influence a decision (though perhaps its should not?) is the occurance rate of false fire warnings. The 332L uses bimetallic switches as fire detectors - the contacts open to indicate a fire so any bad connection, dirt on the contacts etc can trigger a false warning. After many years of complaining they improved the detectors somewhat by encapsulating them in thin metal to keep dirt out and they are now much better, but still false warnings far outnumber real ones.
In a fairly bold move, Bristow departed from the flight manual emergency procedure for the 332L -the RFM says to pull the red fuel shut off lever, at which point of course that engine stops. Bristow EOP says to use the SSL (fuel control lever) to bring the engine to idle, then check for signs of fire. This gives further opportunity to spot that the wrong engine has been identified, before moving the SSL to shutoff, checking for signs of fire again and then pulling the red shutoff lever (after that the fire drill is the same as the RFM). It also gives the opportunity to detect that the warning is caused by a hot gas leak rather than a fire. We continued this concept on the 332L2 and now the 225.
Even though the false warning rate may be high, of course if a warning occurs during an engine failure (as the original poster was proposing) you can be pretty sure its genuine! Otherwise, if there are no other indications / smells etc should one shut down an engine and fire the bottle just because a simplex system tells you its on fire? I would suggest that you should, but only if the rest of the flight can be sucessfully continued on 1 engine.
HC