Good question! Parenthetically, to the best of my limited knowledge, the only time I have ever seen a player injured is when he is fouled...
Your observation is a good one. My understanding is that every time a player is fouled when taking a shot, he has a chance to get an injury. Then the engine calculates how long the injury is. That length of time is then immediately reduced, depending on the level of your doctor (a higher level doctor gives more of a reduction). If the injury is reduced enough, it may be like he was never injured at all.
The thing I really do not like about this system is that shooting fouls are much more likely to occur off of missed shots. It is very rare to see a foul after a shot is made in BB. So the key to avoiding injuries is to have your players make their shots... Or just take fewer shots in general.
Run of the Mill Canadian Manager