If you have some reason to believe the deal is not on the up and up, that is different. I have not seen any indication that the "improver" who spent all the money restoring this vehicle was not a good faith purchaser.
http://apps.dmv.ca.gov/images/vr/regcard_w_arrow2.jpg
You have sent in registration forms that did not include the VIN?
I never have.
Where I grew up, people found out they had bought a stolen car fairly frequently when they went to register it.
The guy who fixed this car up lost it while trying to ship it to another continent.
I suspect he knew it would be discovered if he tried to register it.