If they're going to claim causality for vaccines->less Alzheimers then yes, they need pretty close to 100% confidence for that because this is the sort of thing that gets translated into mandatory government policies. What they have here is literally nothing, it's just a correlation. They don't have any evidence of a causal relation, and they don't have any suggested biological pathway either. It's malpractice to assert causality given such a total absence of evidence.
Moreover, as a killed comment elsewhere in this thread points out, it's very likely that they made a mistake somewhere. This claim is absurd on its face. A 40% effect size is enormous. Alzheimer's is tracked very closely and there has been no change in incidence over time:
https://ourworldindata.org/grapher/prevalence-of-dementias
Flu vaccines on the other hand have become far more prevalent over the last 20 years especially amongst the age groups most at risk for Alzheimers. So, where's the impact? There isn't any. If flu vaccines really reduced the risk that much then we'd see it in the actual numbers, as a 40% reduction is hard to hide.