I'm pretty sure that turning people into stone because of what is on her back is a lie. I think it has to do with it tarnishing her "beauty" and doesn't want anyone to see whatever it is.

As plot progress goes, I think Luffy and her will team up, and she'll hide Luffy in her ship while she accepts the request to witness Ace's execution. That's how Luffy will sneak in to save him.