There's a federal park near me with only one road in, they kicked all the campers out and barricaded the road. Now, you could sneak in walking or riding a bike probably, although so far every day I've seen a couple rangers in trucks sitting at the head of the road....I guess they are essential employees working for free at the moment. But my assumption was that they are liable for this land. Those rangers have arrest power, can give speeding tickets and charge you with DWI, etc. Letting people on the park land when you can't assure staffing to normal levels of safety and security is probably too big a can of worms. Obviously some parts of parks will always have inherent natural risk or danger and its theoretically absurd to shut people out from open space, but I imagine some level of accountability is what's at issue here. Possibly also opening up the park to unchecked vandalism or other bad behavior that would normally be prohibited for the good of the park. Dumping, unauthorized hunting, the list probably goes on and on. These lands were preserved for us, but the flip side of that is the park service is tasked with protecting the parks and the visitors, so without staffing they can't fulfill their mission and its better for everyone to shut it down.
Just responding to the generalization about open space that "belongs to us man", didn't read about the park in the article. I've heard a number of people railing against shutting people out of nature and shit, but there's more at work than that realistically.