From those, looks like RC planes are prohibited everywhere in Colonial National Park (good thing I never tried to fly there when I was living in Virginia). But look again at Death Valley. Looks like they're only regulated at one specific campground. I didn't see anything prohibiting them anywhere else.
Maybe we should get a list going of what national parks allow RC planes and which don't. It varies park to park. You just have to check the rules for whatever park you're going to be in.