Who says not to drink distilled water? You get nutrients from food, not water. The purest and cleanest water is the best. Distilled is pretty much the purest you can get for water, and treated with UV, gets rid of bacteria etc...which is usually part of any water treatment process/purification.

If you want minerals, flouride and other nutrients, take a multi-vitamin, brush your teeth with flouride toothpaste, or eat better foods.