Only the immune system ever 'heals', in any case.
There are some interesting interpretations of "medical cure rates" in the book, Innumeracy by John Allen Paulos.
It's a fool's errand to argue effectiveness of very different approaches to human health, generally - too close to religious 'arguments' to generate more light than heat.
I do know some folks who avail themselves of certain of the diagnostic procedures of allopathic medicine - but choose other methods for treatment. Generally this means - eschewing the automatic prescriptions for the popular Pharm-chem nostrum usually offered - but paying attention to the tests for such as (say) bilirubin levels, other measurements which give hints about the health of various specific organs.
(Exceptions of course - for life-threatening massive infections and the like). Inflexibility is usually a bad thing. Trauma - AMA techniques are superb.
I've met people who have 'beaten cancer diagnoses', and other ailments in this way - but anecdotal evidence.. is never convincing and much of the data we try to use to investigate - - see book above, and others.
Good luck - there simply is a dearth of means for honestly evaluating the many approaches, and only in a Heinlein novel shall we find a fairwitness. Availability of decent practitioners is ever a problem in any locale. In Murica, you have to find a local network and evaluate the words and the personalities. It's different in other countries, though none is immune from frauds too.. {sigh}
But it is a fact that many - rarely visit a clinic or MD. I am one such - but how much of any personal history may be ascribed to luck? genetics? karma (!?) so always and everywhere:
It's a crap shoot. Good luck.
Ashton
PS I have heard Weill, know some others with experience of his approach. I'd go as far as to deem him both genuine and probably wise. It couldn't hurt to investigate, in any case. Even your own attitude is a determinant of what approach has best chance of working. (I know much more clearly what techniques I mistrust, and why - than how to select the 'best' one - though I understand a few of those 'whys', enough to work-with anyhow)