Broken clock syndrome is very easy to "pull off" in medicine because medicine is incredibly complex and it's all risk calculus. For even the most benign or life-saving drugs, you can conjure up examples of how they've killed people. That includes vaccines, unfortunately.

So these people have a leg to stand on. It's a wooden leg (arrrg) but they have a leg. Of course they, and their supporters, are never doing any kind of statistical analysis or risk calculus. The the "risk" part is the thing that really, really matters. I mean, we have chemotherapies which have a very high chance of fucking your shit up or even killing you. But untreated cancers are fatal, and sometimes very quickly. It's all nuanced.