1. People who get the seasonal flu shot are more likely to get flu
Some people never get the flu, because of natural immunity or because they don't spend time in close proximity to infected people. These people are much less likely to get flu shots.
Conversely, some people are much more prone to getting sick, due to poor health, close proximity to infected people, or whatever. These people are much more likely to get the flu shot.
So in the sample group, you would expect more people who got the flu shot to get this new strain of flu. That doesn't mean that the flu shot caused the flu.
2. People who get the flu shot are more likely to be diagnosed with H1N1
This past spring, most people who got sick with H1N1 got mild cases. Most were probably not even diagnosed. The people who were diagnosed with H1N1 are probably those people who go to their doctor more often. People who go to their doctors more often are more likely to get the flu shot. Therefore, of the people who got H1N1, those who are diagnosed are more likely to have had the flu shot.
Correlation does not imply causation.
This sort of research can suggest lines of laboratory research, but it means little without the research. And yes, that applies to all the other statistical health studies we read about in the newspaper.
Unfortunately, immunizations have become the hot topic of people who are paranoid about the medical profession: people who hate doctors, or mistrust science in general, or think BigPharma is manipulating health issues to boost profits.
As for myself, for most of my life I got the flu every year, usually getting sick as a dog and missing a full week of work or more. Every year since 1997 I've had a flu shot and in that time I haven't had the flu. Ontario has now decided to delay seasonal flu shots till after the H1N1 shots, and that increases my likelihood of getting the flu. So I feel I have a personal stake in this. For those who don't want to get flu shots - fine; as long as they stay away from other people when they get sick, they can do what they like. But as a public policy, flu shots work, and shouldn't be delayed until the middle of flu season on such a questionable and preliminary study.