The power of the placebo effect is often extremely underestimated and not well understood. It can be an incredibly effective treatment. People often associate it just with doctors mollifying patients who had nothing wrong with them, but its far greater than that and can massively help the brain and therefore the body to fight genuine illness. There seems to be more acceptance these days that there are strong links between mental and physical health and I remember reading about the power of the effect in Ben Goldacre's 'Bad Science'. Weirdly, trials have even proven that telling physicians that they are prescribing drugs rather than placebos can further increase the benefits. Goldacre is absolutely no fan of the pseudo-science of homeopathy, but he does discuss in his book the huge benefits that can be gained from ensuring that patients are made to feel cared for, valued and listened to. Treat the person as well as the condition and any treatment can prove to be far more effective, something that alternative therapies often have the time and resources to do far better than the NHS does.
The power of a placebo may well work sometimes, if the patient thinks he/she is actually gettig a medicine which will cure them. The logic doesn't work when applied to babies or very young children who don't even have the vocabulary to understand 'This'll make you better'.