Correlation doesn't imply causation but causation always implies correlation.
The claim that national databases of reports of symptoms occurring just days after a vaccination "cannot be used to infer" anything is just obviously not true. Of course they can be used to infer things. That's the justification for collecting the data in the first place, to enable such inferences. To believe nothing can be inferred from these databases requires you to believe that almost all the reports are spurious noise. Some are spurious for sure, just like some COVID deaths aren't really deaths from COVID. But a lot won't be, especially given that it takes quite some work and dedication to file an AER, and some databases like VAERS are moderated (that's why reports turn up in huge batches).
What's happened here is that the medical establishment has decided that vaccines are going to be considered safe no matter what, but, they have the problem that in the past there were problems and thus such databases are written into law in many parts of the world (like the USA). So they're trying to convince everyone that the databases are useless and so dominated by noise no conclusions can be drawn at all, even though in the past, that wasn't true. Additionally, no evidence for this claim is presented. So people outside the establishment go looking at the reports and this freaks out TPTB, who then insist that the public shouldn't look. It's not very convincing.