I have rented points for a stay, and we did not have to pay for parking.
I have also stayed on the hotel side and not paid for parking by showing my DVC membership card, but they actually had to note that in the computer
(As opposed to stays on points, regardless of whether or not the member themselves are staying, the default for the computer appears to be to not charge for self-parking since they did not ask for my membership card when I was staying on someone else's points.)