Market based health care dilemma

Here's a dilemma I've been thinking about after yet another health care discussion (YAHCD) and some recent commentary from David Frum

As is well known, the US doesn't match up well with other nations in comparisons regarding some fairly basic health indicators, e.g., life expectancy, infant mortality, etc. See the report linked in this post. When faced with this fact, defenders of the current US health care system have been known to argue along these lines: "There are a lot of contributors to these factors in addition to medical care. Things like diet, lifestyle, environment, etc. all play a factor." Many then go on to argue that Americans have worse diets and more sedentary lifestyles than much of the world. So, suppose we accept that. Doesn't this fact actually undermine an important arguments against socialized medicine, i.e., the moral hazard argument? If people aren't forced to pay the costs of their health care, they lose an incentive to be healthy and avoid the need to access expensive health care. But, in fact, nobody pays more for their health care than Americans do and yet this moral hazard has no positive effect on their willingness to remain healthy and avoid the need for health care.