Per Wikipedia...
“Sole governance is provided by the Baxter State Park Authority, consisting of the Maine Attorney General, the Maine Commissioner of Inland Fisheries and Wildlife and the Director of the Maine Forest Service.”

Aren’t the salaries of all three of those individuals paid by tax dollars? Sounds like the Park Authority works for the citizens of the State of Maine. So, I would think the “their” in “their park” is the citizens, not the Park Authority.