That's all true, which is why a reputable physician wouldn't prescribe a placebo until he'd exhausted all other possibilities. But in the end, if you have a patient with inconsistent symptoms who has no testable problems, you might prescribe a placebo. Let's face it: the patient's reaction to the placebo can be as informative as any other tests the doctor may have done.
The key point, though, is that the placebo is not prescribed lightly but only after a thorough familiarization with the patient. And this may (possibly, should) include a psychiatric analysis.