Ya I'm skeptical about that. My tap water is hard city water. It has chlorine bleach, flouride, and a lot of calcium in it. Calcium builds up in my sink faucet, stains my sink, and builds up in my water heater. I'm not putting that in my battery.
When I lived in another city with cleaner tap water, I did use tap water because I was in high school because I didn't know any better. It didn't cause any short-term battery problems with a year or two, but I don't know if it might have affected long-term battery life.