There are two separate questions here that have to be disentangled:
1. Does it work?
2. Why does it work?
The answer to the first question is clearly yes, fasting increases health and it shifts the metabolism from a carbohydrate based metabolism to a fat based metabolism, sparing muscle tissue while consuming adipose tissue.
But the fact that the above is true and well documented in no way proves or, even in and of its self, provides particularly strong evidence, for the theory that it improves health by cleansing the body of "toxins" that the body is unable to rid itself of otherwise.
Maybe people are healthier after a fast just because they're leaner - they have a superior fat to muscle ratio, and the body consumes its own less useful cells such as benign tumors and internal scar tissue - in addition to making use of adipose tissue.
Similarly what people believe to be 'healing crises' where they rid themselves of 'toxins' may be attributable to other biological phenomena associated not with their pre-fast 'toxic' state but with fasting. The most obvious is that these are withdraw syndromes not from toxins consumed as a child or adolescent, but from fat, simple carbohydrates, and caffine consumed recently that produce physical and psychological dependence. They could also be side effects of the well documented metabolic changes undergone during a water fast.
So, in short, to believe that Water Fasts A. produce a positive physical outcome and are healthier than ultra-low calorie diets B. transform the bodies metabolism and physiology, does not entail C. that the health benefits come from removing toxins rather than simply removing unnecessary tissue rapidly and with minimal nutrient and muscle loss.