In NC, if you can paddle a canoe or kayak down it, it's considered 'navigable in fact, if not in practice or used for such.' Rivers that are navigable in fact, are able to be accessed by the public. As such, if you can paddle it, you can move up and down the river.
However.... "the right of navigation gives no license to go and come through and over the riparian owner's land without 'let or hindrance.' Similarly, those navigating a river have no right...to land upon and use the bank at a place other than a public landing without the consent of the owner, for the banks of a navigable stream are private property." One source states that the law does not go so far as to say that landowners' rights end at the water line... "As the Supreme Court noted in State v. Baum, "we are not prepared to say that a land owner would be liable to criminal prosecution because he happened to put a Watergate across a creek up which otherwise an idle hunter might be able to pole a canoe..." (128 N.C. at 604)
The way I understand it to be is that if you can find a lawful launch point, you should be able to paddle the river... you may just not be allowed to get OFF the river anywhere other than a public launch. Now... where the Deep River becomes Randleman Reservoir, I do not know. My bet, based on how the PTRWA has acted in the past, is that they will try to tell you that you cannot paddle the river anywhere that they own the land around it... you may need to contact an attorney to study where the river becomes designated as 'lake' and becomes therefore in their jurisdiction. They will probably assume that to be in the same place where their land ownership takes place, but in NC, landowners do not own the river that runs through that land, just the land itself. PTRWA has the reputation of being mean and nasty when it comes to fighting these types of things, but that is by reputation and outside my personal experience. I do know they are very picky when it comes to bank access of Randleman Reservoir, and to take a boat above the pump house at the Groometown Road bridge is to incur a talking-to by the lake warden driving over said bridge in his truck.

If I were a canoeing enthusiast, I would probably have an attorney take a look and provide me with written evidence of where I have the right to paddle, because I would not be surprised if PTRWA tried to bulldog me into believing their version of it whether it's based on law or not.
Clear as mud? Let us know if you find more definitive answers.