As a music teacher I have assessed many students at that level, and as a performer I know pretty well what stage fright is. So I completely understand these feelings.
Some of my best students suffer from stage fright more than the rest of them.
My hypothesis is that the richer and deeper the message one can and want to express, the clearer her awareness of being far from her intention and, therefore, the bigger the chance to make mistakes.
The is certainly unfair. Better students may fail more than average students because they are better in their musical thought and musical capabilities.
Other ways of evaluating musical performance would be more adequate. One would be to collect recordings (with no post-processing) that students could prepare outside the stage with professional recording tools. The live performance assessment is still necessary, but not the only measure.
The gap between playing excellently and doing so at the stage is huge, and extra musical factors play an important role.
For doing well in live concerts you need specific preparation, you need to know and play by heart and fluently everything, of course. Then, you need to train on different stressing scenarios particularly designed to test that you can keep playing so. Finally, you need self-confidence on your own skill. Some people find useful to nurture their self-esteem; others (me among them) prefer to cultivate humility: what matters most is the music I'm playing, not me. The ideal is to become completely transparent at the stage so that the musical essence passes through me as it should sound.