"correlation-only-evidence" as Paul will know, not only suffers from the notion that "correlation-is-not-causation" [ which itself is actually questionable, since , correlation, while not the same as causation, IS highly correlated with causation! :) ] . But: here we have a more basic problem: Many of these side-effects are way too rare, statistically, to even unambiguously allow for "correlation-based evidence" in the first place.
Thus, there are clearly too rare to be of relevance for population health. Much as you should not prohibit self-driving cars only because of some of those spectacularly dumb accidents with Tesla - because statistically, overall one can expect less accidents with self-driving cars.
So what do scientists do in such cases where adverse events of drugs/vaccines are too rare even to establish a correlation? It helps to have a mechanistically plausible explanation - wherein each step of the molecular/cellular/physiological mechanism is a rock-solid fact.
I have tried to come up with such a mechanistic explanation in the case of one of he most frequent (still very rare, and harmless) side effect of mRNA vaccines: Myocarditis.
See the detailed reasoning here (more educational):
