There are thousands of people who have, say, seizures every day. If the proportion of those who have recently received the vaccine and have a seizure is statistically significantly higher than those who have not received the vaccine, there may be a causal relationship. If, however, the rate of seizures among vaccinated and unvaccinated people is similar, a relationship is unlikely.
The article says:
"To defend itself, Dr. Butler [chief of the swine flu vaccine task force at CDC] said, the C.D.C, has compiled data on how many problems like heart attacks, strokes, miscarriages, seizures and sudden infant deaths normally occur. And it has broken those figures down for various high-priority vaccine groups, like pregnant women or children with asthma. When vaccinations begin, it plans to gather reports from vaccine providers, hospitals and doctors, looking for signs of adverse events, so it can detect problems before rumors grow."The emphasis on this point stems from several sources. First, the 1976 vaccination program against swine flu had horrendous problems with Guillain-Barré syndrome as well as deaths that were attributed to the vaccine. Second, anti-vaccine groups are much more prominent and vocal now than they have ever been, and these groups may pose threats to the credible information being put out from sources such as CDC. Third, it's just plain confusing. It's hard to understand, especially for a public getting information from multiple and possibly conflicting sources.
So all those who are reading this (which isn't many), spread the word! There will be illnesses and health events that happen after people get the H1N1 vaccine. But most of these events are likely to have occurred anyway. CDC will be closely monitoring health events to determine whether they are caused by the vaccine or not, rest assured.
Here's another article in the Washington Post about the same issue.