For me I would have to say it was a control issue. At least in a car you have the sense that if something bad happens, there is something you can do about it... try to swerve out of the way, or wear your seatbelt to reduce the chance of injury. But if your heart is out of whack, you're out of control and there's the perception that you could die in your sleep or drop dead and there's nothing you can do about it.
In reality, by getting your checkups and keeeping your health up you are 'putting on the seatbelt' and really lowering your risk of anything bad happening to you. But it's harder to perceive in the immediate sense, I guess. I don't know if it's about perceived control to everyone else, but that's how it was for me.
Also, the kind of anxiety I deal with is in defiance of rational thought... it's very hard to battle it with logic. That's not to say that logic doesn't help... it does, but for me, it's not the sole or even necessarily the key tool, I also have faith, and I make an effort to keep my stress levels down through behavioral means. I inherited this tendency toward anxiety, and I don't think I'll ever be rid of it forever, but I do my best to keep my dragon tamed.