I actually think the author is misunderstanding the quote from the OPM. A shutdown does not mean that each agency has to save as much money as possible. It means they cannot spend any money or create any debts at all (with some exceptions).
Even if it would be cheaper and better for everyone to pay all the staff to keep it running, that's not necessarily allowed.
This sounds crazy, but the federal government really isn't designed to operate without a budget.
Hi, I'm the author! Yep, you're correct - I ended up cutting some explanation at the beginning, and that means it makes less sense if you don't already know how appropriations work. (I have a poli sci degree, so I'm not that lucky.)
This is part of the reason why 'what to shut down' is a complicated question. For example, some sites remained up even though the main portal linking to them went down, so you could only access them if you knew about it already. Other sites were able to stay up in entirety, but froze support/updates for everything but a few critical portions.
Even if it would be cheaper and better for everyone to pay all the staff to keep it running, that's not necessarily allowed.
This sounds crazy, but the federal government really isn't designed to operate without a budget.