A high level doctor will not prevent injuries from happening, though it will reduce the length of the injury. When an injury occurs, the skill level of your doctor is then crosschecked to determine how long your player is out for. High level doctors might see your player returning to action immediately after the game or maybe a one week recovery, a low level doctor might see your player out for 3-4 weeks. So the skill level of your doctor does not affect the frequency of injury, but the severity of it.
Please take note that all quotes from me are not fact but an opinion based on several factors. Unless someone with a BB prefix in their name comes out and states the inner workings of injuries, my opinion will change should new facts present themselves.