His comments are way off the mark. The recent advances in neural network training are not strictly due to convolutional neural networks, but rather the discovery that gradient descent works remarkably well on training multilayer neural networks when using modern hardware. All of the best performing pattern recognition techniques in speech, image recognition, and natural language processing now utilize "neural networks". A neural network is nothing more than a poor name for a non-linear statistical model, and if you like one with a hierarchical structure (which is made possible strictly due to the non-linearity).

I don't think that anybody in the research community (except for maybe an occasional crazy) believes that neural networks have any biological significance beyond inspiration. NIPS (Neural Information Processing Systems) has been a reputable venue for work in statistics for some years now with no confusion over the idea that "Neural" does not mean a precise (or even imprecise) imitation of biological neurons.