Both man and canids were cursorial hunters. The teamwork between men devising the hunting strategy, with their faster compatriots implementing encirclement of large prey, brought greater success. The tamed wolves faced less risk avoiding a direct take-down of aggressive game, and men found more opportunity to use larger weaponry suited to prey size. Thus, a natural synergy developed between the two species, both which practiced pack hunting.
Wolves became domesticated when men would toss them pieces of cooked meat from the fire.
Before that, there was no synergy, no compatriotship.
The relationship came first because of the smell and taste of cooked meat.
With all due respect, your theory attributes more adaptability to wolves than they are capable of...even now.
It was cooked meat that transformed wolves into dogs.
Humans are runners. When they don't run, they die.
When our knees and feet give out, we can resort to biking or swimming to continue our physical and mental (and, perhaps, spiritual) need for physical movement.
Humans are designed to move.
Stop moving and you will die shortly thereafter (or be so depressed that you will wish you were dead).