Why do employers believe the troublemakers at work?

I have a coworker who is trying to get me fired although I have done nothing to create this animosity. I've attempted to make friends with her and she pretends to be cool witth me but she comes into my work area and changes the settings on the machine I have been igned while my back is turned causing it to mess up on me. Sometimes she does this right in my presence. If I attempt to tell her to stop--- it comes to a point where I would have to physically restrain her in order to stop her--- which will get me fired. She doesn't deny having done any of this when the supervisor questions her but she makes lame excuses as to why she did it when there's no reason for her to be out of her own work area. Because of this, the supervisor has told her to stay out of my work area on 2 occasions which she has ignored. Going over the supervisor's head only gets me deeper in trouble because I have no union. The supervisor finds nitpicky reasons to mostly fault me in her presence but agrees with me behind her back. However, I have been told if I bring the matter to her/him again, I'll be written up. Why do supervisors do this??? She has a history (20 yrs) of trouble making and personality conflicts with other employees. I am a hard worker who is never late nor do I miss any days of work. She even disrespects the supervisor's authority by working for other members of mgmt behind the supervisors back because the two of them can't stand each other. She doesn't deny doing that either and the supervisor gets enraged about it--- but there's no consequences. (She has time to do this because she gets the easy sit down job everyday)( medical excuses for not being able to work on machines that actually require work.) Please help me out I can't get another job because of the economy.