Right so this is basically the same situation as what we've had in the New Forest for decades - big black cats, nobody believes you, end of story. Over here they call it the Beast of Exmoor or whatever flavour of county they fancy, but the sightings are identical. Large, black, low-slung gait, moves faster than it should.
My money is on escaped exotic pets from private collections, or possibly a breeding population that's been established longer than anyone in officialdom wants to admit. The Blue Ridge area has enough remote terrain to hide something like this quite comfortably.
What I'd want to know is the tail length and the way it moved - those two details separate a genuinely big cat from a massive domestic moggy or a misidentified dog. Did anyone get any footage or even a decent photo?