If you're looking at VAERS then this statement is objectively wrong.
VAERS records every medical event that happens within 6 weeks of any vaccination and does not establish causation.
Some people don't associate symptoms with the previous vaccination, don't go to the hospital because symptoms recede, etc. Sometimes health care workers are overworked and can't be bothered, or assume someone else reported, etc.
Databases like VAERS and EudraVigilence do indeed suffer from both under-reporting (due to patient apathy, and other reasons) and over-reporting (by design, even events with unrelated caused are included). Therefore analysis of such data takes a lot of care, skill, knowledge and effort.
There are ways we could actually increase the trust of the public in such databases.
By allowing selfreporting but separating reports into validated by a physician and not validated, by default only displaying validated. And grouping reports based on patient so that a selfreported incident and a report made by a physician are not counted twice when referring to the same incident.
By allowing patients to verify that a report made on their behalf by an intermediary (physician, national agency for EU) was included into the publicly accessible anonymised dataset.
By improving the UI/UX of the publicly available dataset (for EU, the Oracle made interface, while serviceable, is suboptimal).
By improving granularity for the age variable. (when investigating the under/over 30 difference in heart issues risk for mRNA vaccines, I found the granularity of EudraVigilence unsatisfactory)
By tracking/allowing public access to extra variables. (I found no way to investigate the theory that heart issues caused mRNA were linked to improper administration. A way to filter/categorise based on facility, date and time of vaccine dose would have been helpful)
There are options we can pursue, but these being state institutions, improvements take a lot of time. We are not a pull request away from doing better.
It didn’t seem worth the trouble or expense to try to do anything about it.
That is the kind of underreporting.
A second kind of underreporting is having only very mild symptoms which would only be caught with a timely test.
There's a legal penalty for incorrect/false reporting, i.e. reporting = risk.
In the current contested environment, there can be institutional pressure against reporting.
This statement is also objectively wrong. VAERS has no data for unreported medical events.
When I last checked the data, the risks of Covid-19, particularly the risk of severe infection and/or "long hauler" symptoms, seemed to outweigh the risks of vaccination by ~10:1. But that was several months ago, and I am wondering if/how things have changed when it comes to booster shots and omicron variant.