Health, first of all, I am not an anti-vaxxer. Most if my children are vaxxed, besides one who almost died after the first dose
But who’s the one who is not telling the truth? Did you actually read the letter signed by the Rabonim you are quoting? There is not a word in that letter about vaccinations. It just says that if one is sick ch”v, he need to go to a doctor. It doesn’t talk about vaccinating a healthy person.
However, the two letters signed by many Gedolim testify that Reb Chaim holds we don’t need to vax, and schools must accept non-vaxxers are being ignored.
Reb Shmuel is also a pretty big Gadol. Or is that only when we agree with him?!?