You can never deduce the cause of any disorder from it's mere presence.
A review (Connors, 1993) found that
"around 30% of eating disordered patients have been sexually abused in childhood, a figure that is relatively comparable to rates found in normal populations."
Patients with eating disorders have been victims of childhood sexual abuse just as often as non-patients. So you might just as well say that not having an eating disorder was caused by sexual abuse! Sexual abuse simply does not distinguish patients with eating disorders from the rest of the population.
The review continues:
For some patients there may be a direct link between sexual trauma and eating pathology, but in general sexual abuse is best considered a risk factor in a biopsychosocial etiological model of eating disorders.
In some cases the eating disorder might in fact have been caused by sexual abuse. But in most cases the patients were either not abused at all, or the sexual abuse was only one of the contribution factors that allowed an eating disorder to develop. Examples for other such factors are certain personality characteristics or genetics.
What you did – forcing someone to admit to childhood sexual abuse – is highly unhelpful, especially if this person has acutally suffered through it.
What you can do to help this person is help her get professional help. And again: Don't force anything on her. Suggest it, find addresses and telephone numbers, if that research seems to put her off, find reports of patients who have profited from a therapy, if she does not believe in a positive outcome or does not recognize her problem, propose to accompany her, if she is afraid to go, help her keep her appointments and adhere to the treatment (medication, eating rules etc.). But remember: therapies only ever work if the patient herself is motivated to go through it. Force is counterproductive. You can only offer support, and if that offer is declined, there is little you can do.