Why do you assume that the government would be interested in tracking anyone's innocent enjoyment of a toy in their own back yard? It's not as if there were enough government receivers or personnel available to capture every limited-range RID...
Your contact apparently isn't very knowledgeable or doesn't know how to conduct an online search. Tell him or her to type 14 CFR 108 in any search engine. The proposed text, more than 600 pages of it, has been published in the Federal Register...
You might be surprised how thoroughly border agents can conduct a search when the spirit moves them. And when they're done tearing everything apart, they don't, as a courtesy, replace things where they found them.
National parks don't have a monopoly on scenic beauty, at least not here in the US, and not all of us obsess about what you call the national parks thing. I find many spectacular places with varied terrains over which to fly near my home, some...
If there are still folks selling sight-seeing helicopter rides to tourists, they'd base their operations in Tusayan, south of the park, and fly over the park in Class E airspace like other light aircraft.