Each of the annotated Rap Genius lyrics are used to explain and understand where the original artist is coming from and the point of the site isn't just to let people know the lyrics (which is at best half of the work being used, if you were concerned with the 3rd of the criteria on fair use) but to provide original content that explains everything. I don't think they would have a problem winning, but the will and money to win might be a problem :s
I'm not aware of any more recent case law that might supersede this as it has been a few years since I've been in an IP Law class. Anyone know more?