I think this is the crux of the issue. People like Chomsky argue the same way, that is, sure a statistical model can mimic a phenomenon to an increasingly likely degree, but the question he concerns himself with is "how and why it [language] works that way", not that I can somehow approach it. His example scenario of a filming bees and statistically re-engineer their dance is poignant: sure you get impressive results, but you will never understand why they dance!
Once this is clear, the discussion becomes healthier: linguists continue to try and understand fundamentals; ML NLP continues to try to get impressive, possibly lucrative results. Logical research can borrow from ML results, or re-use them, and so forth, but I agree with Chomsky that it can't be a shot in the dark always, because once you deploy it and pass it some tough decisions to make, well, what then?
I was pleased to see at least one idea, the recursive structures found in his theories, which is increasingly being accepted by people like Hinton, so that's great.