Earlier quoted context omitted.
Correlations do imply a link, though. They don't imply causation, but in the absence of selection bias and with enough of a sample size, it is almost certain there is a link somewhere.
Well let's test this theory out then. Would you say I was being ridiculous if I told you that the number of people who drown in a year is linked to how many movies nicolas cage appears in? 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.