Problems with a job termination

About 10 yes ago my sister, who had stellar patient reviews as a mammography tech was called in and told an elderly woman had come in and told a staff member that she didn't know why the doctor had waited so long to see her since she had breast cancer. Shocked they asked her why she thought that. She told them the girl who did her test told her. My sister, was horrified and stated that under no circumstances would she have ever said anything like that to a patient. It is not her job to report such results and she would never send some poor woman home with such news. She asked who the person was and they would not tell her. They just stated that the woman had been terrified because of what she said. Her track record of excellent patient care and work history was thrown aside and she was fired with an ethical violation. Obviously she was crushed. However to make things worse, the department managers must of discussed it with staff members, because this week when applying for a job at a different facility they withdrew their interest as a person that worked there had worked at the previous facility and said yes they knew her and told the story. This has happened at two job searches this month as this is a small town and many of the same people work at the same places. What can she do when the original facility never even allowed her to "fight" that claim. She never even knew when this patient saw her or how anything she said could have been so misconstrued. She knew her manager did not personally like her, but did not expect such an event. So 2 "colleagues" from the previous facility are still telling this story and she is losing work opportunities. Any ideas would be appreciated.