We don't have to wonder, because we know that reports of vaccine side-effects were shut down at times, on purpose. It didn't matter whether they were wild rumors or well-documented accounts; it's all swept up as "vaccine misinformation".

This suggests a corollary to me: in addition to teaching people how to evaluate evidence, when we are upset that people are getting the "wrong answer", instead of trying to hide from them things that might mislead them, we should help them find the best evidence available.

Anecdotes about vaccine side-effects aren't a reliable way to judge vaccine safety. Instead of hiding the anecdotes, we should emphasize the studies which are a considerably more reliable way to judge.