Not really my area - I'm more of a skies man than a cryptozoology bloke - but I'll chip in anyway.
Black cats in the US are a proper rabbit hole. You've got escaped exotic pets, misidentified cougars, the occasional genuine melanistic bobcat. Half these sightings end up being mundane once someone actually does the legwork.
That said, we get similar reports over here in Derbyshire. The "Beast of the Peak". Gets wheeled out every few years. Personally I've never seen anything convincing, but a mate of mine swears he saw something near Chatsworth that was definitely not a domestic cat. Big, low-slung, black. Whether he's reliable is another question entirely.
The Blue Ridge area is interesting though - dense woodland, deer population, plenty of cover. If you were going to have a breeding population of something that shouldn't be there, that's the sort of terrain that could hide it for years.
What I'd ask:
What time of day was this?, Any size reference in the frame - tree, fence post?, Did you get footage or just eyeball it?
Because ". Big black cat". Without any reference point is nearly useless for analysis. Could be a large domestic moggy at 20 feet looking like a panther at 200 feet. Happens constantly.
Anyone else on here from that region who can corroborate? Would be useful to map the sightings properly rather than just trading anecdotes.