Child birth is definitely not like the movies! Water doesn't come gushing forth like a broken dam, usually the child's head is in the way, blocking the flow My first, the water broke while I was at the hospital, and that one was messy. The other two, barely any came out until the baby came out.
At any rate, this story is definitely fishy. I believe it's possibly she wasn't aware that she was giving birth, but why would you flush the toilet with the baby in there?