This certainly used to be a big problem for me. Although not all of it was down to SA.
I think like any anxiety conditions you'd have a tendency to resort to safety behaviors, which probably would include not wanting to stand out. SA is essentially a fear of humiliation, so it's conceivable to me that you might not want to appear intelligent or knowledgeable for fear of looking foolish. Also if you're anything like me you might be insecure about your intelligence anyway, therefore have a conscious or subconscious need to keep your mouth shut.
As the saying goes "Better to Remain Silent and Be Thought a Fool than to Speak and Remove All Doubt".
That's my take on it anyway, tell me if you think i'm talking rubbish.