Who signed that player with 20+ turnovers? Who made him the starter? Who coached him? Who hired the assistants who coach him? Who runs the schemes and calls the plays where he turns the ball over so often? Who hasn't found a way to correct the turnovers? So yeah, you DO blame the HC.
That and all the other things such as not enough depth to account for the injuries that all teams experience over the course of a season, lack of execution, lack of raw physicality, poor fundamentals such as tackling, consistently missing assignments, etc.... yeah, those ARE the HC's fault, whether it's Kelly, Saban, Urban, or any other HC. The HC is ultimately responsible for all those things: evaluating the recruits you sign, hiring the assistants who develop them, setting the tone for the team, setting expectations and seeing that they get met, seeing that you have enough depth to overcome the injuries and loss of players that all programs deal with, making personnel decisions about who plays, having the right game plan, executing the right plan throughout the game and managing the clock (or having the right coordinators to do so), and having players who execute at a high level on a consistent basis.
If the HC isn't ultimately responsible for all those things, who is??? It's his job to do all those things or have the RIGHT assistants who will do all those things. If those things don't get done, it's on HIM. He either doesn't know how, isn't working hard enough or smart enough to get it done, or isn't hiring the right staff to do and teach those things, isn't teaching or motivating his players correctly, or isn't signing the right players. In the end, it's the HC's responsibility to get it done or take the blame.