Does freedom of the press allow publication of any material, regardless of its content, even if it is proven wrong scientifically? Clearly, there are exceptions to the First Amendment. For example, the defamation law establishes that public officials could win a suit for libel when they could prove the media outlet in question knew either that the information was wholly and patently false or that it was published “with reckless disregard of whether it was false or not”.
What you find in Food Babe’s book, and hundreds of other books by Deepak Chopra, Larry Dossey, Rupert Sheldrake, Dr. Oz, and their ilk is information that is “wholly and patently false,” because it is scientifically false! And their publishers publish it “with reckless disregard of whether it is false or not”.