At 13 I didn't put my daughter on a plane by herself. And when I did at 14 I hired the plane's babysitting service, for $100 each way to make sure she was taken care of.
How well do you really know the family? If one of my cousin's were to ask for one of my kids I would hesitate too.
Some people aren't' organized enough to know how to get the forms, or even what forms she would need, like a medical power of attorney.
And they may not be able to afford a ticket to Chicago. My family lives there and I cant' afford a plane ticket home.
Why not go to her and visit? Help the mom and dad be at ease with her living with you. Then bring her home with you.
And maybe the girl doesn't really want to come and mom and dad are hoping by not saying anything you will drop the subject.
Just some thoughts.