That's the powerful placebo effect, which works even when you know it's a placebo. Homeopaffic rubbish should be stocked next to the candy aisle, not the medicine aisle.
I exaggerated. She didn't swear by her homeopathic doctor quite until the day she died. At 92, she had a bad fall, and ended up in a nursing home (until then, she'd spent around ten years living fiercely independently, albeit within sheltered housing that we'd moved her into from her flat in Glasgow), under the care of her homeopathic doctor, whom she saw as and when needed (not that often - she was an astonishingly robust, if tiny, woman). The fall changed everything, and she spent the next couple of years in a wheelchair, deserted by her pin-sharp mind, and unable to remember anything that had happened up until that point, including me. She also lost contact with her homeopathic doctor, and was cared for under conventional medicine for the next two years. Then she died.