Personally I believe stuttering is mainly a habit we developed. We talk fluently when we're alone because we give ourselves permission to do so. This is similar to the phenomenon that many stutterers can be completely fluent when they're angry. And the fact we don't stutter when we're alone also indicates to me that this "habit" can be changed. After all, the mere presence of others doesn't do anything with our brain directly - if we'd think we're alone (while in reality thousands of people would watching us without our knowledge, like in a weird reality show), we'd be still fluent.