If it were me I'd be sacking people until they started getting a mean adjustment somewhere around 0. I doubt that is what Trump is doing, but the managers left themselves vulnerable to technical criticism.
[0] https://mishtalk.com/economics/in-honor-of-labor-day-lets-re...
Why sack them? It's not like they refused to mean adjust or failed to do so. The numbers came out, and before anybody has even had a chance to question them. Before any coherent criticism as had time to root, the person responsible is fired.
Firing people is not how you get more accurate numbers. It's how you get yes-men.
It is like they failed to do so - there is a timeseries of consistently negative adjustments. The BLS revising numbers down isn't an unexpected event, that is pretty standard for their jobs reports.
It is better to resolve things with a conversation rather than formal action. But if a conversation doesn't get immediate results it is fastest just to move people on at that level of seniority. The competition is fierce and it is more about finding the right person for the job than trying to micromanage performance.
When reality and truth do not matter, why would they want accurate numbers? They do not need the country to flourish, they just need their personal wealth to grow and the rest of the population to remain compliant. From that point of view, shooting the messenger before the message gets out of control makes perfect sense. It is working well enough for many autocratic regimes around the world.
More generally, this is incredibly dumb in many, many ways. Like, the BLS can't control survey response rates, and the fact that Covid has broken the seasonal models for basically every long-run time series is also outside their control.
One could argue that they should be using IRS tax data to figure this out, but that would be a massive change.
And finally, if the numbers looked good, there would have been no firing (regardless of the errors). It's gonna be an interesting Monday on Wall St.