... Like, having an appointment to their dentist ?
It is funny you make dentistry sound as it was like fixing one's car by oneself. We are talking about healthcare, you cannot just assume the bulk of the people within one country are going to invent a new way to fix their own teeth, without having the knowledge and the degree a dentist has.
What is next on your predictions? Once people do not get access to anti-poison vaccines people will figure out by themselves ways to cure the irreversible limb numbing and paralysis caused by polio?
Are you also going to suggest for cancer patients to stop to go through their treatment, so they can figure out how to be their own surgeons and self-extract their tumors? 

I know people of the United States being dumb is a stereotype, but people like you do not help to dispell such stereotypes.