I read it as "everything can be explained with classical physics alone", the same way we can safely assume the Earth is flat for making a small house. We're not going to complicate math by using the curvature the same way we're not worrying about tunneling, spin, entanglement, etc.
That is exactly why I'm skeptical. Photosynthesis involves quantum entanglement. I'd be surprised if quantum entanglement doesn't play a role in consciousness.
Saying that quantum effects are present and saying that the human brain is a quantum computer (or more?) and will get exponential speedup are two very different things.
We have a pretty good understanding of the individual neuron, and we modeled it with good accuracy. We used a very simplified model of it to build deep learning. The problem is the absurd amount of neurons and interconnections that we would have to run to simulate a human brain.
At some point we may find some phenomena for learning that involves some quantum event, but I doubt we have ever to simulate them at the quantum level.