Another consideration is that, without immunity to fire, then healing this way will probably hurt like hell, but that's more narrative than mechanics.
The Friendly/Unfriendly Fire thing has merit. And it reminds me of the old military saying, "Friendly fire isn't." I'll probably play around with the different methods and see what sticks, once the item comes into play.
Alternatively, I'm thinking length of time might be the easiest way to go about determining what fires cause consequences, and which ones heal them. Getting hit with a flamethrower for a few seconds? Severe consequence or death. Being put on a funeral pyre and burned consistently for an hour after being flamethrowered to death? Wake up right as rain.
Basically, make it so that the amount of fire needed to heal is simply impractical to happen during battle.