I don't think UCLA should punish her, first amendment and all that. If they did, there would be lawyers lining up to represent the girl for a big payout.
That being said, she IS going to pay for doing this. I predict she will pay a
very hefty price for showing the world how stupid she is. Everyone on campus is going to know who she is and she will be shunned. Any potential employer is going to find the video, and it will be difficult to find a job after graduation. Hope she likes flipping burgers. Even though she has freedom of speech, there are consequences.
There are rebuttal videos out now. Here is one. He chooses humor as his weapon:
YouTube - White girls in the library