Kathy, if you can make it through the rest of the book, all that stuff gets addressed.
Behan is not saying that each and every dog is an exact emotional replica of the owner -- or else we would, as you say, have multiple dogs with the same issues over and over. And we don't. The temperaments of the dogs certainly play a large role in the behaviors of those dogs!
What he's saying in the first chapter is that if a dog has problems maintaining emotional equilibrium in certain situations, it is helpful for the owner to examine his/her own emotional state in that situation, and see if the dog is reflecting back what the owner is feeling. This isn't really a new concept.
For years, trainers have been telling us that being nervous and apprehensive will make our dogs nervous and apprehensive.
He put that story in chapter one because it's a pretty dramatic illustration of his basic principle, which is that dogs are creatures of emotion and that we can determine their emotional state(s). Certainly we are not the ONLY factor, but we are the determining one.
I think you are right on the money when you say that Pistol's issues with kids are part of his temperament -- he is a dog who is stressed easily in certain situations and that is how he shows his stress. Could you work with him to change that? Sure. But it is not something that is a step-by-step 'do this, do that' program. It is often easier to simply keep the dog out of trigger situations, than to try to re-form the behavior that results from the trigger.
His books are not easy reads by any means, and they are more philosophy than they are training manuals. I find him very accessible and as I said, he has been a tremendous help to me, but that doesn't mean that everyone will find the same things in his work.