Disingenuous is taking this too far. They're paid in arrears, so the fact they've missed a paycheck means they've already done work which ought to have resulted in pay. They are currently without pay for labor they've contributed within the appropriate time-frame.
I was saying, regardless of whatever position I might take in a thought experiment, the US government has acted irrationally and violated an implicitly (and often explicitly) defined contract within our society: I give you my labor power, you give me cash. It currently stands that many government workers are without pay because that contract was violated and they have yet to be paid for their labor, so WP saying they are without pay is a valid statement.
In the meantime they need to make their rent and mortgage and car and credit card payments and their creditors aren't going to accept an IOU. So for the time being, this is exactly like working without pay.
Edit: To adapt Keynes: the market for payday loans can stay irrational longer than you can stay solvent.
Of course, in the Soviet Union, you didn't have rent and mortgage payments to make, bread and vodka was provided through rations, and during the collapse, nobody cared too much if you looted your workplace of anything that wasn't nailed down, or couldn't be pried off, so society kind of stumbled along, despite the lack of wages.
What I really don't understand is why this isn't being treated like the recurring, front-page, every-headline, national emergency that this is.
For bonus points: These employees are forbidden, by law, to do a strike, or perform a work stoppage, or a work slowdown. If CBP actually carried one out, though, this 'crisis' would be resolved in under 24 hours, as every single company in the United States that had an international supply chain would be screaming at the White House to get this problem fixed.