This is a good time to remind everyone (especially the hundreds of lurkers we have online) that this 'shutdown' was supposed to be simply a 17% budget reduction. These departments under the guidance of their specific leadership in the administration, chose to go to this extreme (in most cases apparently, spending more to shut things down that it costs to keep them open).
In the case of the National Park Service, shutdown orders came from the Secretary of the Interior who answers directly to the President.
They could have simply looked for ways to trim their budgets, instead, you get all this drama.