Are you sure about that? I have heard (and I think MH has even said) that it would remove minerals that your body doesn't or can't use, but not the ones your body would naturally produce and uptake.
I've heard it said about robbing calcium that your body needs, but actually it is an acidosis condition that will siphon off calcium, not distilled water.
Water is another subject with a lot of controversy and opinions. All I know there is not a lot of options for truly safe water, and with the controversy about the different methods of filtering, I think distilling is best, maybe mineralizing it with a touch of sea salt, and or adding a drop of oregano oil, which I do also on occasion.
I do have a Pur filter on our kitchen sink, and use that filtered water to make the distilled water. I know it's kind of silly to do, since the distilled water is only the pure vapor, but I had figured it would be that much less residue to clean later.
To convince my wife that it is worth the extra expense to run this distiller, I did use the 'filtered' water, and let her see the deposits and goop that is left in the boiler. That convinced her, right away.