I like what he says about working with the horse that is loose, and standoff-ish , in the pasture. And, the horse that is so worried he is looking 'outside' of the arena example, well, that is just exactly what I was taught, too.
But, I have to say, that walking along, right close to a horse that may have a more 'in your face' ,pushing on you way of being, . . h m m m . . . I think that can build even more such behavior. Especially if while hand grazing, you maintain enough tension on the rope that the grazing horse is in a state of a constant but slight pull on the rope. That can , in effect, teach him to ignore the rope, which I think is a negative thing.
And, matching steps with a horse you are leading could lead to a person speeding up or slowing down to match up with a horse that has a tendency to ignore his handler and run ahead, or lag behind, so again, you may be reinforcing bad habits.