Or what if you had gone to a "lyme literate" doctor and been misdiagnosed with chronic lyme disease? Put on antibiotics for three years (like one of the patients in the story) with harmful side effects, and at enormous financial cost? Then you would have a whole bunch of problems in addition to your mercury poisoning.
I realize that it must suck for the patient, but in cases where no diagnosis can be made I think the best thing a doctor can do is just to say "I don't know", treat the symptoms as much as possible, and prescribe lifestyle changes (diet, exercise, sleep) in the hopes that things clear up on their own, or that some test eventually reveals some useful information. Better to do nothing than to actively harm the patient with ineffective treatments.