only about 2/3 of employment reports received. There is then a first revision in the next month and a final revision in the 2nd month as more employment reports from surveyed businesses are received. All revisions are contained in the monthly release in the same part of the report every month. There is no "hiding" or "quietly over reporting" . It's all part of the process.

I'd imagine there are hundreds of people involved in some way in producing the monthly jobs report... and the reported numbers are traceable back to the original employment surveys. If an administration was putting their finger on the scale to overstate the report, this would leak out and would be easily provable with an audit.