It is a fine line between legal and not legal right now. As the law is written you cannot "launch or land" in a National Park, the law does not address flying over or through a NP - so there is a technical loophole there. However I have had NP Rangers in both Utah and here in Washington tell me that they will find a reason to prosecute drones within the park; endangering tourists/visitors, flying BLOS, harassing wilflife, etc.
And here in the west the NP are huge, so to stand at the border and fly into the park, one would have to be flying BLOS and using FPV to see anything worth filming. I believe this loophole will be closed soon, and the law will read that you cannot fly over NPs.
In Washington the law is pretty clear about flying over or in State Parks - one can only do so within designated RC flying areas within the park. I belong to an AMA endorsed flying club within one of our State Parks - if I fly outside of that boundary. regardless of where I launched from, I can be fined and the entire club can face sanctions.
My god some people just like to scare people to death...
People... in Washington you can fly over state parks... and if you want to start up out side it and fly over, it is fine as well.