One thing I didn't like was the paragraph on how they differentiate words with no formal training. I feel that gives a false impression. Parents usually teach their children a lot about language. They give them visual cues, speak at varying rates, change their own tone in some situations, and so on.
The babies are soaking up the world on their own using one set of mechanisms. They also often receive highly-supervised training from a trusted source. Later, they get formal training on top of that. Even when not training, much of the content they see and hear is presented in a structured way that helps connect ideas. For instance, listening to the radio or TV with their parents would let them hear a lot of structured speech.
Babies are highly trained. They might also do the statistical learning. They're a mix of the two.