I think it's a reasonable response, if there is a genuine concern or uncertainty. They can hardly wait a year and then say "we suspected that ages ago".
But- considering millions and millions of people have been vaccinated in a very short space of time, it would be more surprising if there were no "unfortunate timings", where someone dies shortly after, but would have anyway.
Or, as my mum said- maybe people are getting blood clots, because they have been off work and sat watching netflix for a year... which I hadn't considered...