The during hunting season rule is due to a joint hunting agreement between NC, Va, and the Feds.
The National Forest can close areas off as they please and do restrict some sections of the NF.
The campground is apparently one area they want to ban the carry of firearms and they can do that.
So concealed or open, permit or not, during the General season or not (Dove and early Goose are in now) they have said no firearms. Despite the idea from some that signs mean nothing...the Law Enforcement Rangers can and will arrest you for violating it as well as the DGIF Conversation Police (Game Wardens).
The best place to check on this is with the National Forest district headquarters.
I was looking over definitions of concealed this morning and a fact came up I wasn't aware of.
Did you know concealed meant no one could see it. Interesting what you can learn from the dictionary
Another interesting bit of trivia, having grown up on that side of the mountain and having spent most of my youth in the National Forest in pursuit of the wee beasties.
Many of the locals are scoundrels (A Pox on them) and don't care much for CHP's but carry every minute they are in the NF. I forget how the rascals got away with it though.