This is one of those things that is discussed fairly regularly and people have always had different points of view. Some are quite adamant that the tap water is completely undrinkable and others are equally happy to let their children drink it. We all have to "agree to disagree" on this one.
Like Graham says, the taste may vary from village to village but we haven't had any problems from drinking the tap water on any of the Greek islands we have been to. Of course, we also drink the tap water in the UK so, if we can survive that, we should be OK in most places.
Like him, I have tried the water from the hose at the sanctuary and it tasted like nectar. Mind you, I had just spent a morning in the baking sun shovelling donkey poo, so I would think even the water out of the sterna would have seemed quite appealing!!