When fasting, however, it is not the distilled water that is doing the leaching. It's your cells. This is why most fasting advocates suggest raw fruit juices for fasting and not water by itself, and especially not distilled water, because it does rapidly move minerals from extracellular areas so there would be less re-absorption potential of discharged minerals.
I have to ask, if we can get hydration and electrolytes from fruits and plants, are supposed to be drinking all this water in the first place? If not, then there really is no debate, except that if you're going to add water to your arsenal of tools, I see no other choice than distilled. Filtered water is still a path to Arthritis and other ailments.