The Seuss case would only be controlling the 9th Circuit, and aside from that it really has little bearing on the fact pattern presented here. In this case, the song would still be parodying the Beastie’s song, as the new lyrics still subvert the original lyrics. This is very different than the Seuss case, where Seuss’s style and Cat in the Hat character were used to tell a story about OJ Simpson, and not to comment on The Cat in the Hat itself.
I suspect that at trial the real questions will be: 1) is this a parody, and 2) if it is a parody, is the parodic nature sufficient to overcome the commercial use of the parody not as a product in itself but as an advertisement. I can potentially see a court saying that the parody as an independent piece is fair use, but that using it for advertising purposes is not fair use. Such a finding would be philosophically in keeping with the reduced 1st Amendment protections granted to commercial speech.
