I fall into "rude coworker" territory, but have managed to do really well in my career. Different groups at my company have requested me to move to them, was just promoted to Expert in my software product, and actually just got offered a job with a 30% raise by one of the clients I work with (which I ultimately accepted and start next month).
My secret is that I'm a hard worker and I'm very thorough with everything I do. I take mentoring others seriously, and although I'm not naturally a very patient person, I am always patient with my coworkers and clients.
You don't have to be good at socializing to climb your way up, but you do have to make up for it by actually being good at your job.
Just gonna start out by saying I'm a woman.
I appreciate the premise of what you're saying, but the unfortunate reality is that people often aren't trust worthy and there are people that would lie about something as serious as SA.
Our justice system is broken in many ways, but I don't think this is one of them. It makes sense that we should have to prove any claims we make against somebody else - especially if that claim can ruin their life.