We visited Palo Duro the week after the Winter Apocalypse and I think because of that, the park was a lot less crowded than usual.  It was our first trip in an RV, so we weren't sure what to expect.  (We normally back country tent-camp and are used to a bit more space.)  We booked Sagebrush site 126, and we drive into the campgrounds, we're literally the only people there.  We plug in, get settled, enjoy the gorgeous views from inside the canyon.  There's a nice structure for each campsite over a picnic table, and a fire ring (which we couldn't use due to the burn ban.)  Not 10 minutes after we get set up, a ginormous RV pulls in right next to us.  The way that the sites are set up, our site was facing their picnic table directly, and there was no barrier between our site and theirs.  Some of the sites closer to the entrance of the campgrounds had more privacy, but then you have the lights of the general store to contend with.  We moved around night-to-night, based on the most peaceful section of the campgrounds, and I think because it was so deserted that week, the authorities never gave us any trouble.  Overall the park is absolutely gorgeous and we went on some wonderful hikes.  Highly recommend!!! [But don't stay in site 126 if you like privacy :) )