I've been googling around and its been incredibly useless, with most results being years old, and one of the top results starting out by talking about TESVSnip.

So what is the exact thing that causes this bug, and how precisely do I go about fixing it?

I'm pretty sure it is related to a mod changing a vanilla NPC somehow, but I'm not sure how to go from there.

Any time an NPC's appearance is altered in any way in a mod, the dark face bug will occur if the facegen files are not created and exported in the CK. I believe the CSE has this ability now, however it wasn't really necessary in Oblivion.

To fix, in the CK find the Actor in the object window list, highlight it (the record doesn't need to be open). Hit CTRL + F4. The CK will ask if you want to export facegen files and a confirmation box will pop up when done. Facegen files (nif and .dds) must be packaged with the mod files.