I once had a theory of a sewer rat that came up and changed the wires on an electric fuel pump. The owner swore no one touched the car other than drive it, Yet when it was towed in the fuel pump wires were reversed. Was this car parked over a drain connected to the sewer system? Sewer rats seem very tallented.
Perhaps the fairy ghost of Tattoo pretending to be Roarke hosting Zora? Hmmm, Didn't Grandpa Munster build cars?

I'm still not buying the story.

As for unleaded fuel in old cars. Lead was to cushion the valve seats. Newer cars have harder valve seats. An old engine can have hardened seats installed and there is no more problem. Without the lead, the softer seats would wear, and then leak. When they failed the repair even before unleaded was to put seat inserts (hardened) in them.
If you don't drive too much, too long, or get them too hot they will last a long time. They will always wear out sooner or later. I have seen them wear out in a few thousand, or 10's of thousands without the lead.

One thing the owner is telling me is that the car belonged to his dad's friend and that the friend moved the car through at least two or three states. Wouldn't it be possible to run a title search or registration search to prove the mileage then? Aren't there ways to do this. I seem to recall seeing some ads in Hemmings or somewhere that offered this type of search service.

I am not an expert, but here is my two cents worth.
Do some work, get some history. Go talk to the friend the seller is telling you of. Get receipts, any and all receipts from whomever owned the car.
If I ran into a 68 roadster, and IT HAD THE ORIGINAL CHALK MARKS ON IT, I would dissect it very carefully with a qualified NCRS judge, and expect to pay out some money for this, then make an offer. If all checks out, find out the value, and then decide if you are going to invest another 10 to 15K or more, in the car to make it right.
If it is a high dollar car, what is it doing in a carport with weeds growing up in it ?
Check it out, but as one post said to you, "If this is what you want, go for it".