They have a fixed methodology and they also revise it as data comes in - usually after the report has been released for one or more months (see [1], [2])
Your counterpoint presents citations from the year 2019 and circa 2012.
OP there posted that they were now cheesing the numbers "for years" - seems to me "for years" might cover the range 2020 (COVID) - 2024, but not your citations.
Anything that says under the post-covid administration they aren't cheesing the job numbers?
So if we think maybe there's some kind of recession in the 2020-2024 time range it might be expected to see a series of downward revisions.
The more tender point is whether these ongoing downward revisions are simply the nature of the beast, or if someone is pressing their thumb and cheesing the numbers a bit to give the impression of no-recession. This is a tender point because some of the unemployment metrics are sus i.e. "people who have been looking for a job for 1-9 weeks, but not more, and it's a full moon on a Tuesday". The more that diverges from (100% - <Definitely employed %>), the more that definition of unemployed is cheesing it. But if the numbers are getting tuned up over here, it's natural to suspect the same party is tuning up numbers over there too.
These numbers have paper trails which would require large conspiracy among civil servants who have really no reason to care about fudging numbers... and if they had this conspiracy operating why would they reveal this at all? It would require an oversight investigation of some sort beforehand.
Besides (not) being told "this is how we're counting", there are incentives that align with functional overstatement.
A weak example is keeping people on payroll who may not have active contracts. There's no reason to purge them if they're eligible to resume working (within the allowed period, which may be, say, 12-18 months), but it's not strictly fair to count them as being employed in the same way as a traditional 12 month FT hire.
Last year, we purged over a thousand people from payroll who hadn't officially separated. Unusual, but not abnormal. Who would call that a conspiracy?
I think it's convenient to lie in aggregate, especially when "job creation" and high payroll counts loosely correspond to economic growth and if not eligible voters, then at least tax revenues.