The fraction of Americans who believe they have good health is higher than the fraction of foriegners who believe they have good health. It doesn't follow that Americans believe they have the best health in the world. They might not know how other countries do, or be using a different scale to foriegners, or believe foriegners are unduly pesimistic, etc.
My European coworkers take sick days when they get headaches, and go to the doctor because they get headaches "frequently" (about once a month). They consider the slightest inconvenience or pain to be a massive health problem. Not that this is necessarily true of all Europeans (though thus far it's been true of every European I've yet met to some degreee...), but Americans in general, and particularly men, have a more rugged and independent attitude towards healthcare, and have a considerably wider spectrum encompassing "good health." A broken rib is an inconvenience, not a health problem.
Of course, it turns out they're actually last among developed nations in real health outcomes.