Well I read about that experiment long ago, but that particular link had been lost in a computer crash.
From what I remember is that the distilled water retarded the plant growth in comparison to the runoff water.
My understanding is that distilled water lacks ability to carry oxygen because of the lack of minerals.
I would never drink distilled water ever. The best water for drinking is the natural spring water. You can find the differences about types of water in the water debate forum.