Post Hoc Ergo Propter Hoc
Many millions of Americans will get sick this year. A couple of million will get very sick. Hundreds of thousands will die. It happens every year. But this year tens of millions will get the swine flu shot. Shortly thereafter some will come down with whatever it was they were going to get anyway. And many of them will blame the swine flu shot. After all, they will have been healthy, then have gotten the shot, and then have gotten sick. Obvious, and obviously wrong.
Wrong and obviously dangerous. If a vaccine health panic erupts people may be frightened into not getting vaccinated and that's the real danger. So public health officials have developed a plan to deal with the expected outbreak of bad causal analysis. You can read more about it here.