But how do you retroactively prove that the patient didn't have asymptomatic COVID when they got vaccinated?

Or they simply developed CFS/ME around the time they were vaccinated, since the two are both poorly understood and look virtually identical. Hell, long COVID may just be a specific cause of CFS.

At the same time I wouldn't discount the idea that the vaccine could cause it in susceptible individuals or under specific circumstances either. We simply don't really have any understanding of what long COVID and other post viral syndromes actually are. (We don't really understand viruses that well, they aren't even alive in the conventional sense)