Your body doesn't work that way. "Detoxing diets" are pure superstition – which toxins are those supposed to be anyway?
From [1]: "The 'toxins' usually remain undefined, with little to no evidence of toxic accumulation in the patient." This fits your claims perfectly...
[1] https://en.wikipedia.org/wiki/Detoxification_(alternative_me...
http://ehp.niehs.nih.gov/wp-content/uploads/121/2/ehp.120548...
"The studies discussed here indicate that AT (Adipose tissue) plays a central role in POP (persistent organic pollutants) toxicology. This role is complex and may seem paradoxical. Indeed, there is evidence that AT is protective under conditions of acute or subacute exposure to POPs. Storage in the lipid droplets has a buffering effect and prevents the persistence of high blood levels of these POPs and also prevents high POP exposure of other more sensitive lipophilic tissues such as the brain."
Want to help your body shed toxins? Drink some water, and your kidneys will get rid of them. The view that fasting will flush them out of your system appears to be wrong, though.
Is this something that can be spun around to the point that it can be claimed water fasting results in detox? I don't know, but I suppose there is all around healing and rejuvenation during this time.
It's also good to give the body a rest from constant digestion, so it can see to other things, and as cravings are reset during the fast, it's an easy transition (afterward) to whatever diet you actually want to follow.
There are many things that detox the body (liposomal vitamin C (liposomal mainly due to the high dosages needed), liposomal glutathione, ashitaba, chlorophyll, Centrophenoxine, magnesium oil spray or magnesium lotion, mercury chelators like spirulina (unless you have amalgam fillings), etc).