This is a popular summary of Chomsky's thesis that was put down decades ago, when cognitive psychology was at its infancy. Now we know a lot more on how babies learn the world and language (do a Google search on "infant statistical learning") and most evidence points to the fact that they employ algorithms that are mainly statistical in nature for learning.
"Children learn language much faster than it seems possible for a "blank" neural network to learn." This is a very strong statement that has no mathematical or computational proof AFAIK. It had no proof when Chomksy first put down that thesis either, it was an axiom of his. BTW, belief in a specialized language faculty was not universal, even in the past, esp. some philosophers of language disagreed with this view.
#2 is simply wrong. Children are corrected when their grammar is off so they do get to see incorrect sentence structure. It's questionable if children could learn language from only watching TV, but that's not the standard learning environment.
PS: I am far from the first person to point that out. At this point they are treating it as an axiom because they continue to believe it despite the disproof of their premises.
"Children learn language much faster than it seems possible for a "blank" neural network to learn." This is a very strong statement that has no mathematical or computational proof AFAIK. It had no proof when Chomksy first put down that thesis either, it was an axiom of his. BTW, belief in a specialized language faculty was not universal, even in the past, esp. some philosophers of language disagreed with this view.