Distilled water can't carry oxygen? I find that hard to believe. Solubility of oxygen in water is affected by temperature and pressure, not purity that I am aware of. I could be wrong, but how does that effect plant growth? I'm not a botanist.
Your link suggests dangers of long-term use. I've been drinking distilled water for 5 years and have never been healthier. I also know many people with similar experiences who have consumed it longer. Why do think that is?
I would never drink any water I didn't have the ability to control what goes in it. Natural spring water commercially made or tap water is rolling the dice (in my opinion) and I have serious doubts you could verify its natural. Even if it was, you're then assuming the rock minerals are fully absorbed/utilized and never collects in extracellular tissue spaces (kidney stones, lymph debris, calcium plaque on artery walls, etc). How do you suppose such conditions form in humans?