Lying about data is unacceptable. Recommending a vaccine is another thing if severe reactions are rare, again, an issue with policy.
I’m more skeptical of claims that Covid pcr tests are false positive prone—design and testing would be trivial, and many labs, like literally dozens, would be cross checking the primers and ringing alarms if they sucked, for example. Literally should take less than a week to have a robust pcr assay for any given target of interest.
Now, some 3rd party testing services may be sloppy and contaminate samples, but most labs will handle it well with standard practices in place. Can’t see this being a widespread issue that would skew data too much. Unless the false positive you refer to means you can detect dna from “dead” noninfective virus, which may be true but at the time, when blocking transmission was key given we knew little about Covid effects, policymakers are more likely to lean on the side of caution.