It is not just pit bulls. Most dogs, under certain circumstances will act out. When I was little, my mother's dog (I disturbed him while he was napping and he was startled) bit clean through my upper lip (actually tore my lip in half). Thank god when I went to the hospital, a plastic surgeon was on duty and I do not even have a scar.
Pit Bulls are known for wanting to make the master happy. They will do anything for their owner. I am sure you have seen the Dog Whisperer... if the owners are nervous nellies, the dog will be too, etc. I really do think it is how the animal is raised. I have raised many many animals... not a one was ever vicious. Trust your daughter, and go and meet the dog for yourself.