I have gone through your question as well as the details of the stages of purification in a Zerowater filter. Rest assured that it is safe, and there would be no problems like leeching minerals from your body. You may safely continue using it for your family. I have also gone through Mr. Mercola s articles and also the youtube videos. I do not think that you need to worry about it. Let me assure that distilled water is actually not meant for drinking and I myself would prefer such a filtered water as compared to distilled water for the purpose of drinking and domestic use.