Analog computers and the Church-Turing thesis
First of all, the authors seem to be confusing two different thesis: the Church–Turing thesis and the Cook–Karp thesis. The first concerns what is computable, and the second concerns what is computable efficiently.

According to the Cook–Karp thesis, all reasonable "strong" computational models are polynomially equivalent, in the sense that they all polynomially simulate each other. Equivalently, every reasonable computational model can be polynomially simulated by a Turing machine. Quantum computers are a counterexample to this thesis, since they appear to be exponentially more efficient than classical computers. However, they are not a counterexample to the Church–Turing thesis, that is, using quantum computers you can't compute anything that you can't already compute with a Turing machine. We can also formulate an updated Cook–Karp thesis, stating that all physically realizable computational models are polynomially simulated by quantum computers.

Several physical models of computations have been proposed as challenging these theses, but under scrutiny, they all seem to not violate the Church–Turing thesis, or not to be more powerful than quantum computation. Scott Aaronson proposes to consider this situation as a "law of nature". However, as far as I know there are no theoretical arguments supporting these theses other than the inductive argument that all models which have been proposed have been shown to conform to them.