Translation:The young doctor makes music behind the hospital.
Shouldn't "the young doctor is playing music behind the hospital " be accepted?
Do doctors earn so little that they try to bring in extra money through street music?
I try to imagine this scene, with a young doctor trying to compose music in the backyard of a hospital, among ambulances and other specific stuff. Hmmm.
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.