People probably do, but it's not necessary, and can even be harmful. She may fill up on nutrient free water instead of nutrient rich bm. Saying that, I can't believe that a few sips of cooled boiled water would hurt.
It does sound weird at first, I think because we find the idea of drinking (cows) milk when you're thirsty odd as adults. Think of bm more like one of those isotonic sports drinks but designed especially for your baby: it's better and more easily absorbed than plain water.