You'll see in my comment and your quote that I don't say the brain can't compute. I agree, the brain can compute. But that doesn't mean it is a computer, because computing is an ability. People can do many other things aside from computing, none of which rely on computation, for instance they can imagine, which is the ability to think new thoughts. Computers can't imagine because all they do is compute: that's their programming. No amount of programming can produce imagination. Computation and imagination are categorically distinct as different intellectual powers and abilities.
You are conflating an ability with ontology. We know what a brain is. It's a collection of fatty material with neurons that do not explicitly fire exactly like a computer. Key word there is like. Church-Turing built a model of computational logic off of intuitions about the brain and formal mathematical logic. That's it's not provable doesn't prove your point; it removes any distinction between it being right or wrong: because it is a model (lets make something like the brain).
That an industry was built on computation doesn't prove anything. We know computation is an ability. For instance it's also something we can do with abacuses. We could have built an enormous industry on building elaborate abacuses. We built computers do be extremely fast at computation. We didn't build computers to be brains.
You'll notice, if you read the review, that the author of the review repeatedly cites cognitive neuroscientists, even evangelists of the singularity, philosophers, psychologists, and zoologists, who have published at length on this topic and repeatedly critcise and disrupt the simple idea that the brain is a computer or an algorithm or even a machine. An entire branch of philosophy developed off of Ludwig Wittgenstein to counter the computational model of consciousness. Numerous books in the Philosophy of Mind argue that the assumption that the brain is a computer is not just unsupported, it is logically nonsensical.