There's a confounder lurking (multiple, actually). I'd love to have a causality arrow here, but we don't have one. Get vaccinated for the thing the vaccination is for, certainly, but I don't think the cohort of people who are up to date on their vaccinations is anywhere close to the cohort that has ignored or doesn't have access to vaccines. Which cohort do you think pays more attention to their health? Their food choices? It's called healthy patient bias and it's everywhere in these lay press headlines. It's really non-news if it's observational association.
You raise a good point that is so often overlooked in news stories. This is the reason that double blind studies are so important.