Ritual is correct, poor quality water is the sole reason for using distilled water. But, what makes poor quality water for human consumption does not necessarily make it poor for painting with. The primary concern with painting water is water hardness - the quantity of dissolved calcium, magnesium and carbonates. These form the scale that appears on the insides of kettles. Distilled water has most of these buffers removed. So even if the water in your area is quite potable, it might not be suitable for painting.
Mineral water, due to dissolved content, is likely to be very poor for painting. Filtered water should be quite acceptable, because the resin filters purposefully remove the chemicals that harden the water. Distilled water can still contain traces of chemicals with a low boiling point, like alcohol, but they are unlikely to affect painting.
A litre of distilled water is dirt cheap at any pharmacy, and will last a long time.