Anyone who follows college football and basketball has read of instances in which it becomes public that a struggling coach has been asked to make staff changes, and they do. AD's routinely review the performance of assistants with the head coaches, and will make recommendations of varying levels of firmness, just as a CEO does with department heads.
The more the program is struggling, the more firm the recommendation is likely to be. By the same token, if a program is doing very well, the AD is probably going to take a hands-off approach and not mess with a good thing. It's no different in that regard than any other business, really.
And, I've personally been involved in a professional capacity with a situation in which a Division I head coach was told by the AD to make staff changes. No, I can't and won't tell you what coach or what program--but if you don't realize this happens, you're not paying close attention.