A single personal story almost always has a greater impact than a statistical value. Convincing people to vaccinate their kids is difficult; science has the numbers, but the dark side (the side that convinces parents to expose their children to unnecessary risk of infection) has anecdotal stories that stir people's emotions. I think that it has something to do with our society's demand for personal experience. You apparently can't have a credible opinion unless you've experienced whatever you're opining first-hand.
Anyone can have an experience, but the most important thing is taking the knowledge gained from that experience and putting that into a broader context.
So I suppose we have two options: (1) people could start putting their experiences into the broader context instead of valuing the experience itself, or (2) start finding anecdotal stories to go with the numbers. I'm guessing that option two is the easiest path to tread.