Not exactly sure which cars you are talking about. I knew Smokey and Richard both and Smokey built three '66 Chevelles- Mario Andretti for '66, Curtis Turner in '67 and nobody in '68 because he couldn't get it through tech. That one was the closest one got to being banned. Smokey lator sold it to a guy to run the sportsman race and when they found out which car it had been originally they told them to take it home and never bring it back.
Turner set the '67 season '66 on the pole for the '67 Daytona 500 and then destroyed it in a wild crash practicing for the Atlanta race a short time later. The Turner car was checked by one of, if not the very, first of the body templates used in Nascar. When it didn't fit, Smokey went to Avis, rented a Chevelle and broght it back to the track. Guess what, it didn't fit the template either! Seems they used Bobby Johns Chevelle to cut the templates and Smokey's Chevelle was closer to stock that anyone thought. Well, the bodywork was. LOL
Petty's Daytona car was repainted with white panels and run at several other races, including the Firecracker 400 so it wasn't "banned" either. Seems that politics is not the only place where the truth doesn't stand in the way of a good story. LOL