The conventional neural network model neglects the interior of the neuron. Gene regulatory networks for complex eukaryotes are on the order of neural networks in complexity and involve quantum-scale interactions, which opens the possibility of quantum effects being significant. Gene regulation within the neuron affects neural firing behavior and, more importantly, profoundly affects neural growth patterns and thus learning and longer term forms of cognition.
This also neglects the possibility (now considered probable) that more cell types than just neurons are involved in brain activity:
http://en.wikipedia.org/wiki/Gliotransmitter
In short: the brain is not a neural network. Rather, those mathematical connectionist models are just that: models of aspects of the brain. We do not yet know to what extent these other mechanisms play a role, and what their role is. Given their nature it seems in both cases that their role might be more long-term, affecting long duration learning, planning, etc.
It really seems to me as if the most ardent and enthusiastic adherents of the Kurzweilian vision are computer scientists who don't really respect the domain of biology and like to hand-wave away its complexity as "background noise." You can't do that. I say this as a lifelong computer programmer who has studied biology. Studying biology really blew away any notions I had of simple, classical computer programs becoming movie-style AI.
The author is not making an anti-scientific "magic" argument. He is simply pointing out that biological systems are analog, embodied, electrochemical (and thus physical and possibly quantum), nonlinear complex systems, and he is being skeptical about the idea that such a system is going to yield readily to digital computer simulation. I agree with his skepticism.
Prediction: brain simulations will simulate superficial brain behavior but they will not become sentient. More specific prediction: they will get stuck in closed cycle loops. They will not exhibit the higher order motivation, creativity, or learning behavior seen in brains, which is probably because these behaviors emerge from all the real embodied biophysical stuff the CS people are ignoring.