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...
Moreover, do note that all published numbers come with standard errors [2] and 90% confidence intervals, which did include the corrections of -133k and -120k that were made for May and June. The current interval for July is -63k to +209k [3]. Anybody who understood high school stats knows the meaning and implications of this.
[1] https://www.bls.gov/web/empsit/cesnaicsrev.htm#Summary
And I'm not going to bother digging through the manuals to figure out how the BLS is calculating their standard errors, but there is a pretty decent chance they've been calculated assuming that the error mean is 0 when in fact it appears to be biased.
In fairness though, Trump's decision is clearly political, these sort of technical factors aren't important enough to rate an official press release and there isn't a cut and dried case that there is anything wrong with the BLS's methods looking in from the sidelines. But for the last few years they have been too optimistic with their estimates and that does strengthen Trump's case.