I'm not sure where you got this from, but it's incorrect. The FAA doesn't establish any such thing. You are perhaps referring to AIM 7-4-6 but, firstly, the AIM is not law, it's informational. Secondly, 7-4-6 gives information on USFS, NPS and other agency rules, not FAA rules. In this context it refers both to regulatory requiremements, such as takeoff and landing restrictions, as well as the
request to maintain 2000 ft AGL. That's just a request - it's not a NPS rule (as you noted, they don't control airspace) and it's certainly not an FAA rule or NFZ.
7-4-6 (c) calls out the only specific FAA restrictions on flights over a few specific National Parks, and notes that those restrictions are shown on the sectionals, as you would expect.
If you want to confirm that there are no FAA restrictions over National Parks in general you can look at the
FAA UAS data website.
7−4−6. Flights Over Charted U.S. Wildlife Refuges, Parks, and Forest Service Areas
a. The landing of aircraft is prohibited on lands or waters administered by the National Park Service, U.S. Fish and Wildlife Service, or U.S. Forest Service without authorization from the respective agency. Exceptions include:
1. When forced to land due to an emergency beyond the control of the operator;
2. At officially designated landing sites; or
3. An approved official business of the Federal Government.
b. Pilots are requested to maintain a minimum altitude of 2,000 feet above the surface of the following: National Parks, Monuments, Seashores, Lakeshores, Recreation Areas and Scenic Riverways administered by the National Park Service, National Wildlife Refuges, Big Game Refuges, Game Ranges and Wildlife Ranges administered by the U.S. Fish and Wildlife Service, and Wilderness and Primitive areas administered by the U.S. Forest Service.
NOTE−
FAA Advisory Circular AC 91−36, Visual Flight Rules (VFR) Flight Near Noise-Sensitive Areas, defines the surface of a national park area (including parks, forests, primitive areas, wilderness areas, recreational areas, national seashores, national monuments, national lakeshores, and national wildlife refuge and range areas) as: the highest terrain within 2,000 feet laterally of the route of flight, or the upper-most rim of a canyon or valley.
c. Federal statutes prohibit certain types of flight activity and/or provide altitude restrictions over designated U.S. Wildlife Refuges, Parks, and Forest Service Areas. These designated areas, for example: Boundary Waters Canoe Wilderness Areas, Minnesota; Haleakala National Park, Hawaii; Yosemite National Park, California; and Grand Canyon National Park, Arizona, are charted on Sectional Charts.
d. Federal regulations also prohibit airdrops by parachute or other means of persons, cargo, or objects from aircraft on lands administered by the three agencies without authorization from the respective agency. Exceptions include:
1. Emergencies involving the safety of human life; or
2. Threat of serious property loss.