The first case was a woman suffering from prolonged, heavy menstrual bleeding. I don't mean an extra few days a month. I mean 45 days in a row with maybe a week between periods. The bleeding was enough to cause anemia, itself requiring medical treatment. The response of doctors was always the same: birth-control pills. At first they worked, but eventually they didn't. Certain pills, I don't remember which, made it significantly worse.
She finally insisted on alternate treatment. The doctor insisted on another month on yet another pill, certain that her problem was polycystic ovarian diseas despite having found no cysts or other matching symptoms in an examination. It didn't work, so he decided the problem must be uterine polyps and scheduled a dilation and curettage - essentially scraping out the inside of the uterus. He could see no polyps during the procedure, but insisted that they're sometimes too small to see.
It worked for a month. After that, the bleeding was back just as bad as ever. I came along to the doctor's office to help insist on a hormone test. He resisted, but eventually gave in. He resisted more when we wanted a copy of the results sent to us directly - in Florida, it's illegal for a test lab to deliver test results to anybody, including the patient without the doctor's permission. A couple weeks later, the results came in. All the levels were within the normal range, though luteinizing hormone was near the top of what seemed to be a rather wide range. A quick trip to Wikipedia made it clear this was part of the problem[1].
I went looking for a way to reduce the LH level, and quickly found that supressing the activity of another hormone called GNRH would do the trick, and that there are prescription drugs to do so. We brought the test results to an endocrinologist and first waited to see if she saw what I did. She didn't, so I told her. She agreed and wrote the prescription. With a retail price of around $60,000 an ounce, nafarelin acetate is the single most expensive substance I've interacted with, but it beats bleeding to death.
In the second case, I found a treatment simply by talking to the patient on IRC. He had a seizure disorder. The actual cause wasn't and still isn't known, but he had been seeing a neurologist. At one point, the neurologist prescribed gabapentin, a drug that acts an an analog of the inhibitory neurotransmitter gamma-aminobutyric acid. This was effective for about a week, but the patient quickly built up a tolerance. After reading what gabapentin was, and how GABA itself is made in the body, I asked the patient if he noticed a decrease in seizures when he ate foods high in MSG. It turns out that he did. He has been taking glutamine in pill form for about two months now, almost completely suppressing the seizures.
So, is everyone smart enough to care for themselves? Of course not. Are doctors necessarily smarter? At least some of the time, the answer appears to be no. I think most people should see a doctor for treatment of most medical conditions, but the idea of laws that prevent people from treating themselves seems like a fundamental violation of the rights of the individual.
[0] The actual cause of repeatedly coming up with wrong answers may be any number of biases, incorrect uses of heuristics or otherwise bad decision-making rather than a lack of intelligence.