Is my car a Tag Job? Barracuda Decode...

OK, now I'm confused. My mom took delivery in the late fall of 1965. The dealer ordered 3 of them, all the same. The 1966 Model years was coming out and mom did not like the squarish of it.
The Barracuda was Blue with Black interior. It had Formula S badges. It has the rear defrost fan (no heat) for the back window. The radiator core support number is 5202800564 and the Vin is V852548189. No signs the core support has been replaced. I remember it had this 1966 dash too, not the 64/65 dash. Finder tag is long gone when they painted the car black

Dealer was Brewer Chrysler Plymouth in Auburn WA, a 5 Star dealer. Guys were coming from Seattle to order Hemi cars because the Seattle dealer could/would not order them. "Auburn, Little Detroit of the West"
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The nimber on the core support matches the SO number on the missing fender tag and not the VIN tag.