Mine have been drinking distilled water for the past three years. No tear stains, no problems and they are healthy. I believe if you feed them properly, all the minerals/electrolytes they need will be included in their diet. There are lots of myths out there.
Here is some fodder related to the subject of drinking distilled, lots of opinion but there doesn't seem to be a lot of scientific evidence either way. Good links from this page:
[Distilled water for drinking?]. [Med Monatsschr Pharm. 1993] - PubMed result