People will weigh the risk/benefit differently if there is a large cost involved. A doctor says "everything seems to be fine, but I'd like you to go to the hospital to be on the safe side." If you have good insurance or socialized healthcare, there is no question -- you will go to the hospital and get checked out. There is no reason not to, and it could save your life. If you have no insurance, then the question becomes "is it worth the certainty of a huge expense, for a small chance that I have a disease?"

Everyone has a threshold of what they consider serious enough to warrant a hospital visit. When you introduce massive expenses you shift that threshold upwards, which means missed diagnoses and an increase in avoidable deaths.