That’s not exactly true either. The publisher didn’t say it was their mistake. They claimed it was a “fact-checking error” meaning that somebody else made the mistake by providing the wrong fact, such as the author ... except that we don’t really know that it was the wrong information.
Or that someone didn't fact-check their assumption. I've had that happen to me: I write something, an editor assumes it means something that I didn't say (sometimes, something I've been very careful not to imply), and goes ahead and changes it to what they think it means without telling me. If they don't run it by me, it's a "fact-checking error," but it's not based on any fact I provided.