Why should the parents blame themselves for the potentially damaging effect an error in the game can have on the fragile self-image of some young girls? This whole thing is about the wider issue of eating disorders, not being offended. In a world where normal-weight girls feel they have to be thinner, a game calling a normal-weight girl fat is adding to that problem, no?
Yes, it could possibly agitate the problem, but I believe the problem shouldn't be there in the first place. A girl with a fragile self-image should trust her parents' or doctor's opinion of healthy weight more than some random video game she played. I'm not blaming the girl for this, since it's not her fault, but it's certainly not Nintendo's or BMI's fault that this situation exists.
I don't have that low a BMI. In either case a BMI of 18.2 is actually slightly underweight, even for a Japanese person, so it would be incorrect to call said person "fat".
18.2 on the "skinny" side of the acceptable adult BMI range, but for a 10 year old girl, it's almost perfectly normal (look it up). For adults, BMI should be between 18 and 24, where 20-22 is ideal.