Judging by the nice, solid piece of wood that was installed just to mount the pancake box on, I'd say a fan is probably of good guess. Either that, or a really big chandelier.
If I could inspect work like this everyday, it would make my day a lot easier. We can only look at the pictures as we see them and not make any assumptions as to panels and whatnot. Lets give this guy credit where credit is due. I have yet in all my years seen the perfect job.
Would the fixture canopy bring the pancake into compliance?
Probably not. Only if it is listed with its volume can it be used for the purpose of box fill. I don't have my book here, but I know there is an exception in art. 314 (exception 4???) that says that a non-listed domed fixture can be used to deduct up to four conductors and 1 EGC that originate from the domed fixture, but even still I very, very seldom see a light that is listed with its capacity.
In defense of the pancake box, the EC wasn't sure of the finished edge of the ceiling. The were talking about plaster, sheetrock, etc. The are also talking about a large decorative medalion around the box. He can protect the wires using an Arlington plastic extension ring that can be trimmed down and will add cu. in. to the pancake box. We will just have to see on the final inspection.