In my experience, the head coach makes that call that we’re going to try to score here instead of running it out, and may provide a request on what he wants to see (“let’s take at least one deep shot here”), and the OC calls the plays. I’ve seen a lack of HC direction sometimes, like the OC calls a pass on first down and the HC breaks in and says knock it off and run the ball.
Yes, the buck stops with the HC, but usually the OC is designing the overall scheme and the wrinkles for the specific opponent. The HC is responsible for selecting an OC with adaptability and the scheme the HC wants to run.