Why wouldn't this be protected speech under the first amendment? As long as the newspaper believes it to be true, why wouldn't they be allowed to publish it?
I don't think this is nearly the case here, but to answer your question publication of false information with "reckless disregard" for it's truth or falsity is also actionable under New York Times v. Sullivan. NYT does not have to believe it to be false to have First Amendment protections stripped.