I'm not sure that they can. I don't believe patent law provides for anyone by the patent holder to sue for infringement.

Could be wrong, though, but I seem to recall a similar story in the news not too long ago.

I believe they can. Stanford is still the patent holder and is charged with enforcing their patent but they could put it into the exclusive contract with Google that Google is the enforcer under contract by Stanford. Of course when Google's attorneys send out C&Ds they will need to mention the stanford-Google relationship and not misrepresent that they are the patent holder.