I love to perform. While I haven't had first hand experience with stage fright or spotlight avoidance syndrome, I have tried to help a number of fellow band members deal with it.
I don't know for sure, but I think that confidence on stage comes from your attitude. If you know your material well and you know that you are able to play it well, you can walk into that spotlight eager to share your talent with an audience. When I'm performing with a band, we are creating a song together. We play off of each other. I'll throw in a fill that prompts the bass to nail that downbeat a little harder and the rhythm guitar locks in just a bit tighter. I'm never worried about how I look to the audience or what they may think of me. I know the material is good. I know that I'm good. The band is creating something new and unique and I'm excited to show it off to the audience.
Friends and family will say that this is because I'm an extrovert. I know some of it may be due to personality quirks, but I also think that there's an underlying belief at work. I believe that I'm good at what I do. I believe that I can play those songs in a way that is uniquely mine. I also believe that while my style may not be to everyone's liking, that there is an audience out there who will love what I play. Whether or not this audience gets it, I believe in what I'm doing and it feels great.
...but that's just me.