My thoughts on this are...

Perhaps she really does want to stop, but perhaps instead she only said that so that you don't worry about her. If she's been doing it for 13 years then she will need a lot of support in order to stop. She doesn't necessarily need therapeutic help - she needs to work out what is causing the eating disorder in the first place - but independent, non-biased people (such as an understanding therapist) are more likely to help her understand that than a well-meaning, if unknowledgeable, friend (the last is just an example, and not describing you). Since she says it's her issue and that she's fine, then maybe she doesn't want to confront the problem. Perhaps for a starter you could tell her you're there for her no matter what...