So by that logic, Jim Tressel & Urban Meyer would not be part of his tree either. My point is that you are a product of your influence; you are what you learn. So, if you were taught by someone who was taught by Coach Hayes, some of you what you learn - even indirectly - is from Woody Hayes.
Some branches of a tree are thicker than others, and therefore produce better fruit. But a branch is a branch.
Saying that Coach Hayes would have no influence on his assistants assistants is a kin to saying that your grandfather's love of the outdoors is passed down to his son (your father) but not to you. Could you have adopted the same love for the outdoors without your grandfather influencing your father? Probably, but the likeleyhood of your enjoyment for the outdoors increases dramatically because your grandfather passed his passion down to your father - who in turn, passed it on to you.