I'm still reading through the paper/article, but a Turing machine would be the substrate in this case, not the model. I think the question is whether we can model the brain's way of computing in a Turing machine, and then it will follow we can also model the brain. Turing machines are a model of computation, and if the brain's computational model is Turing complete, it will follow that we can simulate a brain inside a Turing machine.