I found the same to be true about accompanying another musician. When I was a teenager, I accompanied an outstanding oboe player from a large city philharmonic orchestra. (just in a practice session, but he gave me nice compliments) I found that "supporting" such a gifted musician really brought out my playing (piano) and I completely forgot about stage fright.

My theory on stage fright - and many here will violently disagree with me - is that it is basically a selfish phenomena. I'm guilty, yes, but when I'm paralyzed with stage fright, I'm thinking more about myself than others.