I recall more then one '65 Rebody I had seen in the mid '70s. The ones I knew of were reported to the Registrar at the time and should be still viewable now in that '65 Registry.
Who's to say that it was limited to only those few cars? One I am thinking of in particular was actually a '66 body. The owner was completely unsuspecting.
Usually the people that get swindled are the ones that thought they were swindling the seller and they had found a "Coupe de Ville in a 'Cracker Jack' box"? '65s can be confusing simply because of the running changes through production. The Registry is very helpful in that regard and if you are going to buy a $400,000 car, would be a good investment? A caution flag should go off if someone is selling one for $30,000.
Patina on a VIN tag fools a lot of folks.