Yes, it's a core. I found a seller on Reverb that makes replacement covers. I'm checking to make sure they will work with the proprietary PRS covers.
The other issue is that the stock covers seem to be glued on; they don't come off easily. I have not tried to pry them off or assert any pressure as I don't want to break them. I'm trying to find out if they pop off, or if they're really not meant to be removed.