The tap water at WDW isn't that different from municipal drinking water in the rest of the Orlando Area. I drink tap water at home and at work all the time, and I have yet to get sick from it. The flavor is not pleasant if you're not used to it, but I've been drinking "Florida Water" for nearly 8 years now...
As a side note, I remember hearing from Dr. Dean Edell (sp) that bottled water has a much higher bacteria count than municipal tap water. Tap Water across the US is held to fairly stringent safety standards, so you fearing my local water here in Central FL is like me fearing your local drinking water in... oh, I don't know... Oregon.. yes, let's say your're from Oregon. (the water isn't bad there, is it?)