MTrain,
You are right, the factory did built 4 Jota replicas because of demand by customers, but mostly cosmetic. On the one and only original, Bob Wallace massaged the engine with dry-sump lubrication, higher compression ratio, aluminum body panels, as well as chassis components. None of these were found on the other four. BTW Jota was for the FIA, Appnedix J rules, whatever that was at the time.
So, Nick Cage's Jota was a real "factory built" replica. All other Jotas are fakes. Wait, were we talking about Cobras or Miuras?
Here's another of may favorite cars: The Ferrari 365GTB4 Daytona

SHin