The reference to Kirk not knowing how to drive a car is, I believe, from "A Piece of the Action." I agree with you on this point because the car in question in that episode was an alien reproduction of a vehicle from the 1920s. Probably had the clutch on the wrong side, gears arranged differently, who knows; it wasn't even a real Earth car. I, too, think his inability to properly operate this particular car in no way means he was unable to drive any car.
. . . just an old-school Trekker getting by in a newfangled galaxy.