Translation:The young doctor makes music behind the hospital.
I feel there is a slight difference between the accepted one and your suggestion. The accepted one just tells where the young doctor is making (or playing) music.
Your suggestion on the other hand is focusing on which doctor. The doctor (who is) behind the hospital plays music. No, not the one on the third floor, but the one behind the hospital.
So grammatically correct, but with a slightly different meaning.