Never, ever make even inconsequential decisions based on what you read in the New York Times.
It does not matter if it's true or not. The fact that it even could be true (and it likely is) is enough. Rosenstein is second in command at the DOJ and the fact that stories like this happened whether true or not under his watch is proof enough to demand he resign or be fired. Couple the fact that he is now under threat of inquiry and possible impeachment from congress yet he HAS NOT himself resigned makes it clear he does not have the best interest of the President or the American people in mind.