My doctor told me the best way to heal my back was to take a few weeks off work. She didn't understand why I was laughing my ass off, till I reminded her that most people don't get paid time off. Doctors kinda live on the moon in terms of what the rest of us can get
Depression and feeling sad over sad things aren't the same thing. A lot of people who experience depression may not realize that their feelings go beyond just feeling blue sometimes. Really sounds like the doctor is right to raise this as a potential issue.
The doctor likely has a private practice, so without the heinous pressure of working in a hospital and all the money that comes from being part of the medical industrial complex, its no wonder the doctor isn't depressed.