As one of the articles I gave you in my other post mentioned, we get most of our minerals from FOOD. Chet Day mentioned that FASTING using distilled water can be dangerous. Well, that would be because we aren't getting all of those minerals in our food.
MH advocates the orange juice fast, which supplies minerals.
MH advocates drinking water mixed with fruit juice, or as a herbal tea, not water alone.
Yes, drinking straight distilled water probably does pull minerals from the body, the debate is over whether these minerals are helpful or harmful to the body. In any case, if you drink all your drinks as herbal teas or diluted juice, you are then putting minerals back INTO the body, but they are good minerals that you chose.
Mixing in alkaline juice should bring the pH back toward alkaline. Some people like to energize and restructure their distilled water, with electricity, or leaving it out in the sunshine, etc. Those are things for consideration, too.
I got a distiller in December. Even though I was convinced before (or else I wouldn't have bought a distiller), once I saw and SMELLED the stuff that is in only one gallon of water, I immediately couldn't imagine putting those things into my body. Taking EVERYTHING out of the water, and then adding back what you choose, seems to be the best way to go.