These statements are incorrect. For one, JWs get most health care routinely. There is an institutional opposition to the use of blood products, but this also doesn't apply to all individuals and is sometimes circumvented with technology (more routine use of self-transfusions).
While many of the vaccine refusers I meet do belong to faith groups, their rationale is not often related to religion. For example, one of the big groups of devout individuals are those who choose to home-school their children because they don't like turning over control to public schools. I think these are the same types of people who independently research the mercury/MMR/autism rumors as a matter of correlation rather than causation.