The placebo effect is more complicated than your explanation.
In many cases there have been physiological changes recorded upon administration of a placebo.
From the New England Journal of Medicine....
Placebo effects rely on complex neurobiologic mechanisms involving neurotransmitters (e.g., endorphins, cannabinoids, and dopamine) and activation of specific, quantifiable, and relevant areas of the brain (e.g., prefrontal cortex, anterior insula, rostral anterior cingulate cortex, and amygdala in placebo analgesia).1 Many common medications also act through these pathways. In addition, genetic signatures of patients who are likely to respond to placebos are beginning to be identified.2 Such basic mechanistic discoveries have greatly enhanced the credibility of placebo effects. Moreover, recent clinical research into placebo effects has provided compelling evidence that these effects are genuine biopsychosocial phenomena that represent more than simply spontaneous remission, normal symptom fluctuations, and regression to the mean.1
Second, placebo effects are not just about dummy pills: the effects of symbols and clinician interactions can dramatically enhance the effectiveness of pharmaceuticals. For example, a recent study of episodic migraine demonstrated that when patients took rizatriptan (10 mg) that was labeled “placebo” (a treatment that theoretically had “pure pharmacologic effects”), the outcomes did not differ from those in patients given placebos deceptively labeled “rizatriptan” (pure expectation effect). However, when ritzatriptan was correctly labeled “rizatriptan,” its analgesic effect increased by 50%.4 Similar results have been observed when other drugs, including morphine, fentanyl, and diazepam, have been administered openly and covertly and with procedures such as deep-brain stimulation for mobility symptoms in Parkinson's disease.
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