A man found a wrecked Corsair in a swamp in NJ, or maybe it was Maryland. Anyways, he goes through all the procedures to procure it from the gov't, as is typical in WWII and other military wrecks. he then spends 20 years and bookoo bucks restoring the Corsair.
The U.S. Navy still claims title to any sunken Naval vessel or wrecked U.S. Navy aircraft. It doesn't matter if it's in the bottom of the ocean or if you bring it up and restore it. Unless the Navy specifically granted you title, it is theirs and they will confiscate it or prosecute you if you disturb it. They do have precedent and the force of law behind them.
The Navy does occasionally grant title to wrecks. The last time I remember this happening was when they let a salvage firm recover several F4F Wildcats from the bottom of Lake Michigan that were lost during WWII training flights. The Navy kept one (or two?) planes to restore for their museum and let the salvage company sell two others to pay for the salvage operation. Those planes have a clear title and can be resold, etc, without fear.
Now, this is aside from all the aircraft sold off as surplus at the end of the war or those given away or sold as military aid that eventually were brought back. The Navy surrendered title to the new owners in those cases. It's just that for wrecks, even though it's a wreck at the bottom of the ocean, the Navy still says it's theirs. (I don't believe the Air Force follows this policy, btw. They could if they wanted, but I've never heard of them giving anyone grief over the recovery of a warbird)