So far as I can tell, it's a Windows filter driver which intercepts file requests matching a certain pattern and forwards them to TileProxy (or, any program which connects to it). It doesn't seem to care what program sends the requests, and you can see this by looking at the files in Windows Explorer or something when it's running: TileProxy will spit out a bunch of messages about unexpected requests or some such. So I doubt it's the problem here.
My best bet at the moment is something with the static .bgl files that P3D doesn't like. It could be something with them being in an old FS2004 format which P3D no longer supports, or something. I'm not really sure. It definitely reads those, they show up in P3D's "open files" list, it just never seems to actually do anything with them, including the LOD8 ones which should replace the terrain even without TileProxy running.