Do the books specifically address using water as a reductant? My experience is that not even scientists in the field (I worked at reprogramming hydrogen-producing enzymes) have a full appreciation of how bizzare that is.
If that's the conclusion, it's trivially true, since basically you can assign a redox value to every chemical transformation using the nernst equation.
The interesting thing is that IMO the resistance to the conceptual framework behind the way that the mitochondrion works was because it was hard for biochemists to picture the proton motive force (concentration gradient) as a redox potential (it truly is one) because it seemed more physics-ey than biochemistry-ey. Peter Mitchell cleared that up amidst quite a bit of controversy. He had to go to the lengths of setting up an independent research institute to get the work done.