Doctors only very rarely give meds, no matter what E! showed. Remember, E! was TV, not real life. They did a lot of things for 'dramatic reasons' that would never happen in a real hospital. Brackett might stand by and watch the nurse give the meds, but he's not going to do it himself - it's not his job, and he doesn't have the training needed to do it. (Although it's more likely he wouldn't even be in the room. Despite what you see on TV, most doctors don't stand around and do a lot of hand-holding. They're far too busy and they're just not interested in interacting with patients that much.)