The critical words are operating from or on lands and waters. If your not standing on NP grounds you are not operating "from or on" NP land, you're operating from or on the ground you happen to be standing on.
Agreed. Maybe I misunderstood your post:
Operating in my mind would mean you can launch the aircraft from outside the NP and then come into the part and operate it from within the park.
I thought that you meant launch from outside the park and then enter the park yourself to continue controlling the aircraft.