Byzantines called Greek Fire 'war fire', 'Roman fire', 'liquid fire', or 'processed fire'.
They wouldn't call it Greek Fire, that's like a Canadian calling Canadian Bacon 'Canadian Bacon' when not talking about American bacon.
Not to mention that thinking of it as an empire-saving weapon . . . so its so wonderful it can restore the Empire from nothing, but not so wonderful as to actually be employed when it could have kept the Turks out?