Is being underweight ALWAYS unhealthy?

I have a younger friend who is 13, almost 14 years old. She's 4'11" and 75-80 pounds. Which makes her BMI between 15.1-16.2. A "healthy" BMI is between 18.5 and 24.9. I just don't see how she could be considered unhealthy though. Yes, she is very skinny. But she doesn't look sickly at all! She takes dance classes 5 days a week, they do serious muscle building exercises. She has noticeable abs, calf muscles, and tiny biceps. Her whole family is skinny like this. She CAN NOT gain weight. After going to the doctor for a physical and being told she was underweight she ate chocolate ice cream and/or cookies every night before bed in an effort to gain weight. After months of not gaining a pound she stopped because she said it felt unhealthy to be eating that every night.

If she's living a healthy lifestyle (eating right and exercising), and is naturally this thin, does it STILL make her "unhealthy"?