My DD went through a similar thing at the same age, also triggered by a friend who was telling her if she eats x,y,z she'll get fat and die. Basically, we had a chat about 'sometimes foods' and how eating them in moderation will not make her fat. I also addressed it with her school, who had a chat to the girl in question and her parents. It took a while to get her to eat properly but now she's fine.