Placebos have medical benefits even when the patients know they are receiving nothing more than sugar pills. The placebo effect is no longer based on the physiologic effects of the mind.
This is not medicine or psychology, it is spellcasting. Everytime someone says the word "placebo" they are unknowingly chanting an ancient latin prayer of "I shall please." Like a penny tossed into a fountain, the pill shall satisfy the wisher's unspoken desire.
Placing intent on a physical substance imbues it with power.