I could've sworn that I posted a similar picture to this, but I can't find it, so I'm borrowing one of Roth's. It shows how they taped the individual letters of Plymouth:
There were a few brands visible in early episodes. Boss' Caddy started out with its original door mirrors, complete with Cadillac logo, but they later got replaced with aftermarket models. Dixie's Jeep logos were also on show at the beginning, but they were later removed or taped over, despite the car being placed in the show. In 'Mary Kaye's Baby' they even describe Cooter's car as "A 1975 blue Plymouth Fury", but it didn't last.
I'm guessing that they just took the decision not to promote any brands, or it could've been a clearance issue.