We need to forget about breeds. Every dog will bite if they are in a bad enough situation. It is a natural defence. The vast majority of dogs will only bite as a last resort after they have given several warning signs. Breed is much less important that temperament and history. The main reason certain breeds are more dangerous is because of their physical ability to cause more harm (e.g. bigger jaws) rather than that breed's personality or nature.
I have had many dogs over the years, big and small, and I have been bitten several times. Each time it was my fault in one way or another. For example, as a child a terrier bit me on the face when I tried to kiss him on the nose. I had been repeatedly told to leave him alone and after he had backed away, growled, given me plenty of notice. Even then he just did one snap and I got off very lightly. That dog was not at fault and thankfully was not put down.
That is very different from a dog who will randomly or unpredictably attack someone, especially if the behaviour escalates over time.
I have 2 dogs at the moment who are really well trained and have always been gentle. I never allow them to interact with anyone unsupervised and if there is a child nearby then I have the dog on a short leash. I get the shivers when I see people allowing young children to play with dogs, it is just such an unneccesary risk, and the consequences can be horrific. People are deluded thinking that their dog is "good" or that a family dog like a labrador is "safe". Demonising certain breeds actually increases the overall risk to children because we get a false sense of security about the supposed safety of other breeds.
Every dog is a bite risk - some are close to 1% chance, most are in the middle somewhere, some are sadly at 99% - but none are 0%. Every dog owner should understand from the outset that their dog could turn out to be dangerous and they may need to one day euthanise them. If you can't contemplate that then you should not own a dog.
In this case the owner has realised there is an issue, is going to great lengths to identify the causes and address them, and seems very responsible and proactive.
- you never know she might think the baby is a cat 
