This is what I have been told on drinking pure water:
Drinking tap or filtered water, does not have any direct impact on your mineral/vitamin uptake unless you are drinking good "mineral water". Even then intake is minimal, plus most people do not use mineral waters as any kind of significant nutrient uptake anyways. So drinking really pure water would only have an effect on your body at the excessive side of the scale. Pure water will make water intoxication, or Hyponatremia develop faster.
http://chemistry.about.com/cs/5/f/blwaterintox.htm
P.S.
RO/DI coffee IMO tastes way better.
and i'm not sure on this, but in my mind since your drinking water is also powering your bodies waste filtering systems that the purest water will help it work better. I.E. ~1 TDS can absorb more toxins then +100 TDS water.