I get Chomsky's point about the importance of fundamental models and understanding in principle, but I'm confused why it should apply to machine learning.

The problem with Chomsky's knowledge based approach is that it seems to be domain specific. You can learn the fundamentals of music but you can't apply it to physics. You can learn the fundamental mechanics of weather but you can't apply it to psychology etc..

General learning though requires exactly that and there the statistical model seems to be much better because it doesn't run into the domain problem.