False placebo

A false placebo is a non-placebo factor that appears to cause an improvement of a disease. False placebos differ from actual placebos in that they occur regardless of whether the patient is treated or not. False placebos are the "other" things controlled for in the placebo arms of clinical trials.

Spontaneous remission
Spontaneous remission (also known as spontaneous improvement or spontaneous regression) is a phenomenon in which an untreated disease or condition suddenly disappears for no apparent reason. This is one of the ways in which alternative medicine can seem to cure diseases such as cancer (along with misdiagnosis, in which case the person is "cured" of a disease they don't actually have).

The spontaneous remission rates for cancer depend on the type: according to studies done, basal cell carcinoma and breast cancer disappear in about 20% of cases, while the rates for melanoma haven't been studied, but have been estimated to be around 10%-20%. Autoimmune hepatitis goes into spontaneous remission in 13%-20% of cases. Untreated tuberculosis goes away in approximately 29% of cases. About 65%-75% of people with invasive group A streptococcal infections live.

Misdiagnosis
Malaria misdiagnosis is a problem in Asia and Africa. In one study, out of 414 patients going to hospitals using clinical diagnosis, 412 were prescribed anti-malarial drugs, even though 413 tested negative for malaria.

Regression to the mean
Regression to the mean is just a fancy way of saying things tend to revert to normal given a set period of time. Many diseases are self-limiting. Time heals. So, most people will return to normal even if they have no treatment. Regression to the mean, however, can also mask actual efficacy of a treatment, and it's one of the many reasons anecdotes aren't reliable sources of information.