The fact that so many gifted child have sensitivity issues aligns well with Dabrowski's Overexcitabilities and Theory of Positive Disintegration. However, it runs completely contrary to our local school, which assures me that it's not normal for gifted kids to have emotional or behavior problems.
I find your school's perspective interesting. Our district decides whether a student qualifies for GT with testing but also with other factors such as emotional or behavior (perhaps due to prior improper instruction/placement) issues the kids may have due to giftedness. In fact, they have a social worker who comes to the class once a day in the GT class for discussions.