It makes sense to me that it's all about control with her. I wonder whether there's a way to have her take control of her own treatment in some ways. For instance, with my son, we let him choose one treatment a week to take off. It was his choice when to do it--so if he had a sleepover, he could skip the night and just do the treatment the next day when he got home, or if he wanted to sleep in on a school day, he could take off then. The doctors were perfectly happy with that, as it meant he did the other 13 weekly treatments with much less fuss. Kids with CF truly DON"T have enough control over their own bodies, and if this is how your daughter is expressing it, you might need to think creatively about how to let her take control without starving herself.
If the doctors say she needs a feeding tube, you may have to do it--but if you can address the underlying issue and let her gain control in other ways, that would be a happier solution. Good luck with this difficult problem.