Aerobic fitness is not a matter of life and death.
The authors want to paint a distinct line between “exercise training” and “endurance training”; they do not believe that aerobic exercise is necessary to be healthy. They are right about it not being necessary, but I do not like their take on the matter.
Whether aerobic and endurance exercise is necessary depends upon your goals. Obviously, since I am a marathoner, I am not going to do very well in my races if I do not go out and run hundreds of miles. If I was just starting to work out for the first time and my only goals were to lose weight or make myself healthier then I would not worry as much about it. As is, my goal is to work my weight lifting around my running schedule rather than the other way around.