I'm not a doctor, but have recently had substantial orthopedic work. Nuhaus is correct that pinning a broken bone is serious business, and that surgery is no guarantee. However, looking at these xrays, I'd say there is approximately zero need for surgery. This is a clean, simple fracture. Manipulate the two bone segments into the correct position, then set the arm in a cast to immobilize it. In a 20-year-old girl, the bone will heal quickly, in 3-6 weeks.

Slabo, you might be correct that this is a case of doctors taking advantage of a patient's desire for "the best" (at someone else's expense -- whee!) to provide a procedure that is not necessary and also carries unnecessary risks.

Unless the surgery is already done, and the point is moot, you might try to get a truly independent opinion by sharing those xrays with other doctors. Not just for your sake, but for the girl's.