YouTube is (inadvertently) aiding other people in an attempt to harass her, and the only recourse they provide requires her to reveal her full name to her attackers, thus opening her up to offline harassment. Seems like a good reason to sue.
I don't know american law, but to me that would be just as silly as suing the post office because someone sent you a postcard with the message "fuck you".
Anyway, if she sues, won't her name be on the public records of the case?
IMHO she should just host her videos elsewhere. I can't even begin to imagine how many similar cases of internet drama goes on over at youtube every single day.