Cohen has not addressed BuzzFeed’s reporting, and BuzzFeed has made clear he was not a source for its story. Lanny J. Davis, a legal and communications adviser to Cohen, said before the special counsel statement was issued, “Out of respect for Mr. Mueller’s and the Office of Special Counsel’s investigation, Mr. Cohen declined to respond to the questions asked by the reporters and so do I.” He declined to address it after the special counsel’s office released the statement.
The WP is going with the premise the story is true. They're just trying to work out why Mueller would deny it.
The story is fake news.