This doesn't sound like a common scenario, but under the circumstances, it seems like the psychologist is doing the best he can to get a fair and accurate assessment of your daughter. He's obviously picking up that there's an emotional issue that's preventing her from doing her best, so he's trying to work past that with her.
Being upset about not knowing an answer sounds like perfectionism, a very common trait/challenge in gifted children. My DD7 recently asked me why a girl in her GT class always cries when she gets an answer wrong.
