I personally disagree, distilled is best used for a fogger/misting because it doesn't leave hard water stains on glass. You should use tap treated with conditioner or bottled spring water in my opinion for soaking. Distilled water is also much more "pure" than tap water that has sat in the water for a day. Deionized is the purest form of water and is the best, but the best can get easily is probably just distilled water. If you have any evidence that supports that tap water that has been sitting in the sun for a day is the same as distilled I will gladly change my opinion
EDIT: I was typing my post before Bill posted his, sorry to copy you Bill!