Actually, when fasting, the body holds on to a lot more toxins because it is low on vital resources and the kidneys and liver begin to release hormones to retain minerals and nutrients instead of urinating them out. This is why fasting often results in both kidney and liver damage along with enzyme increases.
You posted this same link in another comment. This article does not say distilled water is bad, and only demonstrates that extreme fasting is dangerous, which I agree with.