If so, then you might not actually believe linked is simply a synonym for correlation. I know I certainly would think that was a ridiculous way to phrase it.
Loads of people get the flu vaccine. Enough that I'd imagine the sample size is representative of the population at large. A large number of people also don't get the flu vaccine. So this is a surprising result. Especially since we are injecting a liquid into the people so there could reasonably be some effect we never thought of. Which is the whole point. These people aren't correlating things in completely unrelated fields and claiming a link.
This sort of intellectual looseness is not free. People are learning to treat claims by scientists as untrue, and it's partly because of this sort of press release/paper hacking.
Finding a correlation between two random medical data sets does not mean there is a "link" in any English that normal people would use it. It definitely does not mean there's an "effect" or that one thing "reduces" the other. It might mean there's something worth a followup investigation there, though given the prevalence of non-reproducible p-hacked results in science, also maybe not.
Regardless, before doing press releases and going to the public with such a claim there is a large amount of work needing to be done to actually prove causality. Moreover you'd then want to ask why does such a thing happen when there is no prior reason to suspect such an impact.
I don't see it that way. Nick Cage has nothing to do with Alzheimers. We're not finding correlations with Nick Cage movies and then saying "Nick Cage linked to reduction in Alzheimers".
They are suggesting that flu vaccination may have some 2nd order effect beyond protecting you from the flu. Which could be reasonable, science reporting and poor research notwithstanding.
Either way, the refrain "Correlation does not imply causation" is over used in my view. And I'd rather learn the specific ways the research is flawed.
https://www.healio.com/news/primary-care/20200302/flu-vaccin...
I don't think there's a really killer argument here in the abstract: I personally find it unreasonable to imply causation from any medical intervention to any possible outcome based on just a correlation. Yes, it's more reasonable than Nick Cage being associated, but not reasonable enough. That's a judgement call however. I am guided in it by the massive costs and problems created when scientists claim vaccines are miracle cures without sufficiently robust data.
You might want to read the paper before saying untrue things like that so confidently:
“Mounting evidence indicates that systemic immune responses can have lasting effects on the brain and can influence AD risk and/or progression. A diverse range of microorganisms and infectious diseases have been associated with an increased risk and/or rate of cognitive decline, particularly among older adults, including influenzal respiratory infections [5, 6], pneumonia [4, 7], herpes infections [7], chronic periodontitis [8], urinary tract infections [4], gastrointestinal infections [9], sepsis [4], and most recently COVID-19 [10]. Prevention or attenuation of microbe-related inflammation may therefore represent a rational strategy to delay or reduce the risk of neurodegenerative disease. Consistent with this hypothesis, studies have found a decreased risk of dementia associated with prior exposure to various adulthood vaccinations, including those for tetanus, diphtheria, pertussis (Tdap) [11–13]; poliomyelitis [11]; tuberculosis [14, 15]; herpes zoster (i.e., shingles) [6, 13, 16, 17]; and influenza [11, 18–21].”
Unlike your Nick Cage theory, this has a clear mechanism and is compatible with the understanding of similar effects.
I said "almost certain". What you did is taken a database of someone who made millions of comparisons, such that coincidences that are very unlikely to occur happen via pure coincidence.
Additionally, I said "enough of a sample size". Given that the analysis you're talking about was over 11 pairs of points, that doesn't even qualify as very unlikely.
For those who don't know the reference: http://www.tylervigen.com/spurious-correlations