One problem I have here, though. If the patient's symptoms are relieved by the placebo, then their is not problem. If it's cancer, or some other serious disease, the placebo would not work. He might feel some relief for a brief time, perhaps, but as the disease progresses the placebo effect falls off. Chances are the doctor would not let him go for a year anyway, but have him check back in a week or two. If at that time the symptoms are relieved THEN he might diagnose hypochondria, not before.
And I doubt that any reputable doctor would go right to placebos anyway. He'd have to have some kind of indication from the patient's history before taking that step.