Just for grins can you get the info off the Warranty Plate and have someone on here decode it for you. That would tell when during the year it was built. If it's titled in a state that goes by when sold, I guess it could have been a leftover 63.
I would think it unlikely that "new" Uni's were still being built late in 63 as they had replaced it with the "wrong bed". Another thought, he could have a Uni that someone has "swapped out" the door tag with a 64 tag. Would be curious to see if they door tag and the frame VIN were the same.