This is a common misconception. There are a number of OECD countries who compare quite favorably with the US on health outcomes like heart attacks, strokes, and cancer. (there are many different types of cancer however, and who is better varies) Health systems are generally not rated in a policy perspective by overall health because it is a poor indicator of what is actually happening when people interact with a health system. (ie: if you never even go to the doctor, why should it be counted against the health system?)It's a complex issue and it comes down to how you define outcomes. The data I've seen shows that we do extremely well in outcomes when you look at something like 5 year mortality rates for a given cancer but poorly for overall health compared with other OECD countries.
The bottom line is that we are less healthy because we live less healthy lifestyles. We receive more and higher quality health care but that can't offset the effect of lifestyle factors on overall health. We also spend much more on end of life care which by it's nature has a minimal effect on health outcome numbers. We aren't getting a particularly good value for our money which is why I'm willing to trade lower quality and quantity for lower costs.
You might be interested to learn that recent health research shows that unhealthy people actually cost the system LESS money than healthier individuals. This is because...well.. unhealthy people tend to die before they consume as many health care resources. Our focus on end of life care is most certainly one driver of health costs, but it does not nearly explain the vast disparity in cost vs. quality. Interestingly enough, a single payer system would be far more able to control end of life costs in this way.