That's what I was hinting at. Especially if you exercise a lot it can be quite dangerous. It could actually kill you.
Random from the internet but I think valid: http://www.mercola.com/article/water...lled_water.htm

If you are in a developing country then you typically drink spring (mineral) water or filtered (typically reverse osmosis). It's not common to use distilled water in lieu of tap water. The Aqua Rich stuff is probably for the radioactivity-phobia fringe that thinks that everything in Japan is contaminated including the ubiquitous Asahi/Kirin/Suntory mineral water (Fuji-san sourced) that you can buy for 80 yen per 2 liter bottle by the case.

The German Embassy is probably supplied by Aqua Rich.

I guess some people in the States drink it since it's sold in the bottled water aisle. Getting distilled water in Europe is also a problem. Based on the anti-freeze specs from European car makers they appear to expect that people dilute it with tap water (therefor phosphate free). Tap water is very hard in many places in Europe. In the US most people use distilled water to dilute anti-freeze. (At least I do.)

Japanese tap water is pretty soft. Factory fill Japanese anti-freeze (typically dyed red) is very high phosphate (for corrosion inhibition). But it precipitates with hard water and would be be disaster to mix with hard tap water. Since they don't sell distilled water for anti-freeze dilution then it is essential to mix it with soft water in Japan. I would use the "battery water" sold in autoparts stores, but my guess is that nobody does this. The Japanese don't do their own car maintenance anyway.