For the purposes of this discussion it's distilled, because it doesn't have minerals in it. As you say acid rain contains sulfur dioxide and nitrogen oxide. It

For the purposes of this discussion it's distilled, because it doesn't have minerals in it. As you say acid rain contains sulfur dioxide and nitrogen oxide. It can also pick up other gases. Rain also contains carbon dioxide, and rain near the sea also contains some salt. (Then again, distillation isn't perfect either.) It doesn't contain dissolved limestone, granite, or other minerals that might be found in ground water, at least not that makes a credible biological difference. I don't understand your comment about wine - if you distill crude oil you can end up with gasoline, asphalt, and more.