That's true.
Public land belongs to the state or federation and its administration depends on the jurisdiction in question. If it is a state territory, it is the state's scope. However, if it is a federal territory, the administration must be made by the federal government. Both powers have their own land management agencies.
Example of territory under federal administration scope: National Park Service
Example of territory under the scope of the state administration: Anza-Borrego Desert State Park, California.