VAERS suffers from some serious data quality problems. It isn't a representative random sample. No one really validates reports to determine if adverse events were actually caused by vaccination. I suspect that some anti-vaxxers just straight up submit false reports to push their political viewpoint. At most VAERS provides some clues about where to focus real research.
Yes, hence the reference to private HMO databases. CDC VSD (Vaccine Safety Datalink) is not public, sometimes we get data snapshots when CDC is investigating specific adverse events, like blood clots, https://news.ycombinator.com/item?id=27464528. There are people with access to both VAERS and VSD for trend signals, including doctors with private data from seeing patients.
