Very interesting, this. A law was passed decades ago (I think just after the Cuban missile crisis) stating all surplus US military aircraft would be "demilled". This entailed not only removing all the things that went "boom", but also cutting up the main wing spars to ensure the plane would never fly again. Basically all the military aircraft you see flying under civilian ownership (built after 1962 at any rate) were purchased from foreign countries without this restriction.
I think Air and Space magazine was the last place I read anything about an aircraft "escaping" the demill process. That case was an F-104 (as I recall) which was certified as cut up but for whatever reason never actually got cut up. It's just possible that's what has happened here, especially since it would seem the FBI has already given this guy the sniff test.
A potential buyer would also have to deal with the Navy beauracratic machine, no small task. The Navy retains ownership of all its aircraft, right back to the very first one. Ones purchased before their own "mine! mine! mine!" regs are exempt (although I think they tried for those too), and of course there's always overseas, but anything else is Navy all the way. For example, people fishing WWII-era fighters and bombers out of lake Michigan for restoration must jump through all sorts of hoops to get permission to even dive on the wrecks, let alone salvage them. It will be very interesting to see what sort of reaction the fleet has.
Finally, military jets are not Hondas. Even the new "maintenance free" 4th-gen jets were designed with the assumption of a dedicated full-time maintenance crew on hand with all sorts of special tools and testing gear. I distinctly remember a picture in Air & Space Magazine of a man standing next to the maintenance manuals of his F-5 fighter, an aircraft designed specifically to be maintained by the poorly trained mechanics typically found in the third-world air forces of the '60s and '70s. The stack of books was five feet high and about fifteen feet long. And, unlike a race car, if you screw up maintenance on a fighter jet you generally end up dead.
This is not to say operating such an aircraft would be impossible, just a lot harder and more expensive than most people think. From my various readings it seems the stuff built in the Soviet Union is much more rewarding/far cheaper to fly. Those things were meant to be maintained by conscripts out on the frozen tundra and muddy steppe of Russia. Their jet trainers in particular are very popular with the high-performance aviation crowd.