Parts of Mesh Imported to Substance Painter are Entirely Occluded by AO

I am having a problem when baking textures for an FBX file imported from Blender. Certain parts of the mesh have their own texture set (e.g. the section of the mask in the center, random bolts, etc.). When these are baked with ambient occlusion (w/ self-occlusion off) they come out as completely black, which in my mind at least seems incorrect. This is not an issue with all parts that are a separate texture set, just a few.

Attached is the AO view of the model:

Does anybody know what might be going wrong? Thanks!

Dropbox links for .spp and FBX