M.D.
Yea, this is one of those "ti's not you, it's me" situations, and she should be saying it. I think she is to blame. HER work wasn't done right, so she is looking to deflect the blame off of her, you got it this time. Next time it will be someone else.
I'm all for getting along with the people you work with, but I also don't try to be best friends with anyone. This is my first job where I have not connected with people outside of work to hang out, and I'm MUCH happier. My personal life is my own and no drama follows me in the door.
So my point is that I would not ask her to lunch and try to be her friend, I would just keep it casual and friendly in the office. If she can't handle it, maybe she isn't ready for a big girl job yet.