That is, as you note, generally true, but rare exceptions exist. I got a flu shot in the early 'Nineties (because someone I interacted with was on immunology-suppressent drugs for organ transplantation) that caused an extreme cytokine release syndrome that was much worst than any bout of influenza I’ve ever had, and put me off of getting the annual flu immunization for over twenty years. The anticipated 1976 swine flu epidemic (which ended up being less severe than projected) is infamous for a vaccine that resulted in an increase in Guillain-Barré Syndrome of about 1 in 100,000, although epidemiologists broadly agree that even if that risk was known it would have still been prudent to immunize the population to prevent an H1N1 influenza epidemic which could have been comparable in impact to the 1918-19 ‘Spanish Flu’ pandemic.
This and other incidents are why we have (or, at least had) the CDC Advisory Committee on Immunization Practices to review data from vaccine trials and ongoing surveillance to prevent adverse effects from immunization, and this is (or at least, was) arguably one of the strongest review systems in pharmacology. Vaccines have––by far––prevented more mortality and morbidity than any adverse reactions have caused, and next to public sanitation and water treatment are the main reason that we do not have epidemic outbreaks of severe disease every few years even in dense urban environments.
Stranger