"Reduce severity of injury" means that your player will get a shorter length of injury, not reduce the probably of getting injured. I mean if a "broken nose" is 4 weeks regardless of level except that higher level doctors has a lower chance of getting it, it would have been "reduced chances of getting more severe injuries".
I think that there have been quite a few threads that debunks your observation but sadly it's hard for me to pull as a non supporter. Not too sure but I think even BBs had some input on it during the "ask the BBs" sessions.