When the Bat-cars were sent on the car show tours of the late 60s and early 70s, they were covered in velvet to conceal the unavoidable stress cracks, called 'spider-webbing', that appear in fiberglass bodies. I guess a side-benefit of this is you can let people touch the car, and no fingerprints are left in the wax shine. The cars were later stripped and repainted.
I also recently noticed that in the above picture of the velvet car, the rear glass area is missing! A big guess is that this was taken when the velvet was about to be taken off and the body repainted....
...or it may be the #3 car. If you look closely, you'll note the dime-store plastic phone and the absence of 'roll-top' compartments in the dash.

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