I agree. All I see here is: "We know any reasonably smooth function can be approximated by a neural net, likewise it can be approximated by a polynomial. So they're the same!" Imagine how it's going to blow their minds when they find out about Fourier transforms or wavelets!

There are lots of ways to approximate functions; the property of NNs that make them attractive for ML isn't the universal approximation theorem. It's that there's a fast, robust method of training then that's easy to implement, easy to vectorize, easy to parallelize, and easy to customize for different applications.