Beginning and end of story, at least as far as FR is concerned.
As for the parody, that has its own suite of Constitutional protections. Even a Weird Al Yankovic song parody is practically untouchable; add yet another layer for political free speech. I hope Corbis appreciates that you are going way above and beyond what is required.
I wouldn't expect that to be the case, as music and lyrics are in some cases regarded separately at copyright law. As such, because Weird Al uses other people's music essentially verbatum, I'd expect that he'd have to pay for that. If he were to rework the tunes so as to be recognizable parody versions, then he wouldn't have to pay.