Here are the latest National Park Services rules on the matter
This is the specific area of interest that I believe pertains to us flying our drones in those areas.
9. Does it matter where an unmanned aircraft is used for the required closures to apply?
Yes. The NPS has the authority to regulate or prohibit the use of unmanned aircraft from or on lands and waters administered by the NPS. As a result, the compendium closures required by the Policy Memorandum only apply to launching, landing, or operating unmanned aircraft from or on lands and waters administered by the NPS within the boundaries of the park. The closures do not apply to launching, landing, or operating unmanned aircraft from or on non-federally (e.g., private or state) owned lands located within the exterior boundaries of the park. The closures do not apply to the flight of unmanned aircraft in the airspace above a park if the device is launched, landed, and operated from or on lands and waters that are not administered by the NPS.