The inverter has stand-offs on the back of the unit, just like a zero-clearance, high efficiency fireplace which suggests to me that if it were to get hot enough, fire leaving the box might not be the concern, but heat transfer from the box to the adjacent structure. If the box catches fire and said fire were able to leave the box, I'd be worried about the ceiling too. Thin sheet metal is what was to be used with my fireplace.
I'm going to install 1 sprinkler a few feet above this inverter, just in case & slip a piece of hardy cement board behind the hoot side, just in case.
Thank you for your reply timselectric.