I'm not by any means going to recommend this, but I just tested my tap water can compared it to a sample of RO/DI and melted snow from my back yard.
The tap water had a TDS reading of 72ppm, and a pH of 7.9
RODI had a TDS of 1ppm, and a pH of 7.7
Melted snow had a TDS of 2ppm, and a pH of 7.2
But when I tasted all 3, the melted snow was pretty bad tasting.
Oh yeah, I also tested the "filtered" water from my fridge and although it tasted better (couldn't detect the chlorine), the TDS was about the same (70ppm) as the tap water.