If you think about how pure water cleans - you've stripped all of the dissolved solids out of it, so it wants to return to it's impure state, it absorbs dirt. That's why it is supposed to clean better than normal water.
On the flip side, when you drink pure water, it is dangerously low in minerals, and can therefore absorb the nutrients from your body, with obvious results.
There is a condition in trees as a result of reverse osmosis, where tree has its nutrients absorbed out of it, because of lack of nutrients around it. Not sure of the specific's of this, my father-in-law mentioned it as he's a tree surgeon, so it's probably not a good idea to make a habit of drinking pure water!
Also, think of the stuff that can grow very quickly in water that's sat around. Can you be sure that your water hasn't got anything lurking in it? I wouldn't drink from my system, the water is sat around in a hot garage most of the time, without all of the chlorine that the water companies put in to keep it potable.