I agree with the principle, and said so before--I just think it makes for a bad argument to say that people are getting infected from the vaccine as an example of why we need free speech! No, if we could successfully constrain such speech to cases where the distribution was low and the correct information was quickly prompted, then we wouldn't want this kind of thing to be free--the problem is just that we can't successfully constrain this.

At best, it's an example of why we want misconceptions aired so other people with free speech can explain why it's wrong.

I am not sure what you want me to cite to prove that an outlandish claim that isn't being made is, in fact, wrong. I mean, it would be pretty difficult for it to be true and the Pfizer authorization data to be what it is. Like, look at Figure 3: https://www.nejm.org/doi/full/10.1056/nejmoa2034577

But there are literally hundreds of papers afterwards that fail to show infection from the virus. Additionally, New Zealand managed to vaccinate a substantial fraction of its population while maintaining zero Covid which is pretty impossible if people were catching the Covid virus from the vaccine itself.