Ultimately the call was yours and you followed the doctor's advice. You say that she was 'worried.' Perhaps she felt concerned. The sun can sometimes affect us in negative ways, depending on exposure. It can also be too little, sometimes, depending on the season and its strength. All this has been documented and can also be found on social media.
Hundreds of cases have been documented where doctors were wrong. I would generally go with his/her advice but with logic, that is to say, the thing given or prescribed, should appear to make sense. More and more people are reading up on their conditions and challenging doctors.
Please don't do this unless you have to, but I'm saying that it is sometimes healthy to think and even to have a second opinion if you are concerned.
Ultimately, there is value in complimentary as well as allopathic medicine, and like religion, one should leave many windows in the heart.
You can always ask the teachers view or reasons. I would say though, that vit D is proving more and more to be a really essential vitamin, and for many, supplementation in the winter is a good idea. Post consultation and a blood test with the doctor, of course, and the age and history of the individual. Good morning and have a great Sunday!