Well I'm glad you mentioned "the power of the placebo" because that is the only effect possible with a 200C treatment. It is water, plain and simple.
Of course you do miss the possibility that fibroids can go away by themselves entirely untreated especially as a woman starts menopause. While the average age for menopause is around 50 the is a great deal of variation and some women start before even reaching 40. Therefore in your sample of one single person it is entirely believable this had nothing at all to do with even the placebo effect. Without medical history no one could say anything for sure on this one case.
If you go read the literature on treatment for fibroids you see efficacy numbers for the placebo in the 10-20% range. So really it shouldn't be surprising that any treatment emulating a placebo, such as homeopathy could claim to have success. But that doesn't mean it is a great treatment especially when remedies to control bleeding can be 80% or more effective.
http://www.nejm.org/doi/full/10.1056/NEJMoa1103182
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5155051/
Thank you for your engagement @o1o1o1o.
I completely agree, fibroids can and do go away by themselves at menopause, but usually this in the case of small fibroids only. Large fibroids very rarely go away by themselves, hence the number of fibroid related hysterectomies.
Moreover, please do not assume that the other three cases I mention were peri-menopausal or menopausal women.
I note your statistic about the effect of an iron supplement (effective in just 19% of the placebo test subject group) in the paper you cited, as well as the common reported side effects of headache, nausea, abdominal pain and hot flushes in using the drug Ulipristal for fibroid reduction (around 25% of women). Luckily 100% of my patients showed a reduction in symptoms from the treatment I offered, and 0% of my albeit small sample of patients complained of side effects or any 'serious adverse events'.
Your blanket disdain of the power of homeopathy aside (I encourage other readers to test the validity of your statement by a quick read of the many papers published by the Homeopathic Research Institute: https://www.hri-research.org/), it is clear that placebo does work for at least 19% of fibroid patients (around 12,000 women per annum in the UK) and this in itself is worth further investigation.
Whether the options offered to fibroid patients are iron supplements, homeopathy or another 'placebo', all are likely to be cheaper and less distressing to the patient than the looming threat of a hysterectomy.