Yes, what Franken shows is that O'Reilly repeatedly used "we got two Peabody Awards" as a way to argue that his show (I can't remember the name, but not the current show) was not a "tabloid show."

But they had never won any Peabody awards.

They did win one Polk award, after O'Reilly had left the show. His claim is that he mistook the Polk for the Peabody, so it was "just an error." Franken's point is that, even if it was just an error, it happened after O'Reilly left the show, so he can hardly claim "we" won it. And, after Franken pointed out the error, why didn't O'Reilly thank him, and correct the error? Instead, he blustered and complained and harrumphed, and said to Franken "Go after me if you want." So Franken did.

But funnily enough, even though it's gotten the most publicity, that's the most trivial of all the lies the book documents.