I think that completely misreads a comment that was already painstakingly clear, they're specifically talking about the phenomenon of reasoning by anecdote. It wasn't a one-to-one equivalence between LLM driven medicine consultations the full range of dynamics found in the anti-vax movement. Remember to engage in charitable interpretation.

They are closely related. The authority of the medical establishment is more and more questioned. And whenever it is correctly questioned, they lose a bit of their authority. It is only their authority that gets people vaccinated.

“Asking inquisitive questions and thinking for themselves? Must be an anti-vaxxer!”

"My impression is that anti-vaxxers have more issues" - I think you could have left it at that!