> How do we know that all or even most of these "events" are not coincidences but were a direct result of the vaccinations?

One way to identify a signal is to compare against other vaccinations. Assuming that a vaccine doesn't cause some symptom, all vaccines should have the same incidence of that symptom.

Keep in mind that this is the same data that the FDA uses to estimate risk/reward of vaccinations. Submitting a fraudulent VAERS report is a felony and there is no evidence that such abuse is occurring at a wide scale.

If anything, there is likely significant under-reporting. This study identified 10x as many cases of Myocarditis as the FDA estimated based on VAERS data:

https://www.medrxiv.org/content/10.1101/2021.09.13.21262182v...