What you are saying makes absolutely no sense. I also think that you overlooked an important point I made. Let's say you drink mineralized water. The water is pretty much saturated. So when it enters the body it has to RELEASE the minerals it is carrying in order to take up something else, whether it be a toxin or a nutrient. So there is an exchange reaction going on. If you drink a purified water it is more solvent, and so it is going to aggressively look for something to saturate with. Again this can be toxins or nutrients. Instead of an exchange reaction though you just have a grab whatever it can reaction.
And how do you get the body makes its own distilled water? Distillation involves evaporation. The only real "distillation" we are going to see is the evaporative cooling of sweat. And this is not going to do much as far as moving minerals or toxins.
I am really lost on the comment about the body having to use its vitamins and minerals to make distilled water. Distilled water is a purified water. If I took water saturated with vitamins and minerals I would be removing these, not adding them, in the process of making distilled water.