Maybe your girlfriends parents don't support a tourette diagnosis because she is diagnosising herself. If she has insurance, what is stopping her from seeking a professional medical diagnosis? If there is no TS experienced doctor on her medical plan, than gather information on tourettes and take it to her general practitioner and talk to him.
My son is 11 and for almost a year I tried as much natural remedies as possible and they helped a little, but not enough to stop him from licking his desk in school and keep him paying attention long enough to finish his work. We started him on Abilify, he is only on 2.5 mg a day and he went from the school not being able to grade him to all A's and B's and lots of friends now calling the house. I found with doctors that are uneducated in tourettes, you must take contol yourself and ask for what you think is best to try. This medication is not cheap, my co-pay is 50$ a month (200$ a month supply if no insurance and that would be the lowest dose) and you need to read all the side effects and be under a doctors care.
I do not believe that diet is the cause of tourettes; however, believe it is the cause of making tics or emotional behavior worse. It takes dedication to watch what you eat and it will take money and support from her parents because vitimans and tests are expensive. She can do some of it on her own without cost and I would start with the depression because this alone can prevent her emotionally from carrying through with taking care of herself. Sounds to me like the depression is worse than the tics because she could harm herself, but watch these doctors that want to prescribe several medications, one for each of her symptoms. I just got back from a tourettes family camp in Tampa, some of these kids are on 4 or 5 meds. Some doctors are splitters and some lumpers (meaning my doctor lumps my sons OCD, ADD and depression as TS) and he is on one med which helps all of them and I still see from time to time very little of any of them but remember medication is not to make you get rid of depression all time, that's not normal.
Good Luck