That's how you can tell the DoD does that on purpose, to "make it hurt." In the private sector, companies usually rotate the furlough days to minimize the disruption to the business. Obastard gave one order for "sequestration:" Make the cuts as painful to the public as you can. That goes double for the military. Locking out the entire population from the PX is a great way to do that.
There’s no doubt it’s on purpose. At the unit level, we have to make it work somehow, but DoD can play the budget tantrum game all they want.