most likely he holds the “salvage” rights, which means that he can theoretically control who is allowed to dive the wreck, and holds the rights to any property removed from it.
But imagine that a private party owned the USS Arizona.
Would you want just anyone going down there and effectively graverobbing? Or would you want it protected as an historic/archaeological site?
I don’t believe a shipwreck should be “bought and sold: if control remains in the hands of a government.