What i've read in the Game Manual :
Doctors help reduce the severity of player injuries. Once a player is injured, a Doctor will also help him heal more quickly, but the effect is much smaller than the initial reduction in severity. Doctors can have the following specialties:
Taping Injuries: There is a small chance that a player's minor injury can be taped up immediately, and he will be able to return to the game at the start of the next quarter.
So the Taping Injuries speciality will only matter in case of a minor injury during a game, when the injured player could come back during the game. So the speciality has nothing to do with your case.
As for Doc's level, i understand the Game Manual's explanation as a reduction of probabiliy of a real severe injury. That means that a severe injury (a 5 week one) can happen, but with less probability than with a lower doc level.
I do agree that the Game Manual's explanation is not clear about the real impact/calculations that occur about Doctors in the game. But as far as i've been reading the forums, almost everything is about probabilities in the game... and Perpete already told there was no bug in this case ! :°)
Cheers