Part of my information package lists ALL possible persons who may pick up your child. And states that if they are not on the list, the child will NOT be released to them.
In actuality, if there was a serious "emergency" situation, and I actually spoke to the parents (not just email or text) and they informed me that someone else was coming, I would be okay. I would ask for id, though. And if the child was old enough, I would ask for confirmation from them as well.