I wonder too. Is she a work colleague or were you her patient? If it is a doctor-patient relationship, she should have never accepted your friend request on FB to start with. So it should be goodbye and good riddance. Also, if she is your doctor, it is a good idea to find a new one, IMO.
If it’s a work relationship, you have to keep in mind not everyone has a small FB circle of friends. There are people out there with hundreds of friends, most of whom I doubt they know, but many people do that on FB. So what might seem like an intimate friend request to one person may seem like no big deal to another.