I have been trying to explain this to people for years but there are still people that will insist on drinking distilled water regardless. What they need to remember is that water is the universal solvent. And the more pure it is the more solvent it becomes. In fact, ultrapure waters (type 1 water) is actually corrosive. And water does not have a brain to say "I will take the bad stuff and leave the good stuff". It will take whatever it comes in to contact with. This includes vitamins and minerals.
There was a study a while back that found purified waters actually increased the risk of heart disease by removing beneficial minerals, like magnesium, from the body.
This problem is not only with distilled water. It is also a problem with reverse osmosis (R/O) water. This is why silica or minerals should always be added to distilled or R/O water before consumption to reduce the water's solvency.