Interesting Thread..I agree with SASless that the incidence of engine fires seems vanishingly small - probably because the designers are so conscious of the general depression it brings on if you have one!
I think there is a real concern with the integrity of warning systems for engine fires. Spurious warnings abound in certain types if you leave them out in the rain...BUT I've always been taught to regard any such warning as real and do something about it quick. Confirmation of a possible fire can be hard to achieve without landing which isn't much good if you are 100 miles out to sea.
Are offshore operators allowed to divert to rigs in the event? I wouldn't have thought so.
When I was a baby pilot I heard a tale of a pilot of a Wessex 1 (which had a history of spurious warnings) calling Culdrose, "Spurious Fire warning, returning to base" pause 2, 3.. and then the aircraft blew up.