Something tells me that if this young lady does have self esteem issues they won't be solved if she joins this chapter.
If the rest of the sorority feels as you do, they obviously wouldn't be able to accept her as she is, so I wouldn't give her a bid. If you don't like someone as they are right now, save them and you a lot of crap and don't even go there.
Plus, there are girls who lie about BOTH sides of the sexual spectrum. She might be pulling your chain just to see how you react. I know I would.