You need more statistics than calculus to understand the current state of neural nets in Machine Learning, but you if you don't at least know the chain-rule, you're just using library code and not understanding even a basic perceptron.
And from a personal perspective: I've used so much trigonometry in my career (plenty of graphics work) that I'm not sure where I'd be without the time spent on trig and geometric reasoning in school.
I mean, I agree with their basic thesis that stats is important because of ML and the increasing practicality in using statistics and AI to solve problems. But I don't thin what they'd discard is well thought out in terms of what is going on. Nor is it meant to be, it's just a casual interview.