SAS, the question was about a fire in an R22; as far as I know, there is no fire 'light' in that a/c, and therefore the questions assumes sound evidence that you are ACTUALLY on fire!
I think the MANUAL (or at least the CAA supplement) assumes sound evidence that you are actually on fire, but the QUESTION flying shrink has asked actually begs precisely that issue.
If you absolutely know you've got an engine fire, then shutting off the fuel flow is good sense. If you're not sure then it's probably the first step of turning a drama into a crisis.
I may be projecting my own prejudices on the situation but IMHO the original (US, FAA approved) manual is written from a practical pilot's perspective, whereas the CAA not untypically has taken a rather lawyerly approach to the situation - ie. if you know you have a fire then shut it down. Well Duh !
But to show I'm not completely biased I came across an unrelated situation recently where the CAA approach was actually vindicated. To much grumbling from US manufacturers, the CAA insists on a Low Voltage warning light to indicate when the alternator is not working properly. I flew a plank (horror !) in the US recently and fortunately had an instructor with me who spotted that when the flaps were set, the ammeter showed a discharge. Since the ammeter is buried way over on the other side of the a/c I very much doubt if I'd have spotted it on my own, so would have run out of electrics a few minutes later over Nantucket sound. Nice !