I’m sure fire was used both ways, but the firefighters’ badge story is directly from the website of a firefighting organization. They claim that the Scaracens originated using fire as a weapon in war.
Greek Fire was invented by a Christian Syrian Refuge, and used to defend Constaninople against the Muslims in 670 AD.
Under the old definition of Sarcaren (Syrian), the firefighters would be correct.
A Syrian Christian invented it, to burn Muslims.