Ok just read some more of the NC Justice Dept webpage.
It says:
"In addition, this State law has been interpreted to require that a pistol permit be obtained by the reciever of a handgun when such person inherits a pistol as a result of the death of another person. The permit should be given to and retained by the seller or donor of the handgun. In such a case, the permit should be given to the executor or reciever of the estate of the deceased person"
So, I'm an only child, and would be the executor of my parent's estate. I guess this means I would get a permit and give it to myself.
Also, from that reading, where you dont use an FFL for an inherited pistol, it doesn't seem like you'd have to go thru an FFL for a private party transfer either. The seller would just keep the permit (which really doesn't seem like a good idea legally, seems the chances of someone losing the reciever permit are pretty high).