On Thursday night, the New York Times put a “BREAKING NEWS” alert across the top of its homepage and sent out an accompanying push notification. The siren was for a story entitled “N.R.A. Suggests Trump May Retreat From Gun Control,” written by three Times reporters. It began, “The top lobbyist for the National Rifle Association claimed late Thursday that President Trump had retreated from his surprising support a day earlier for gun control measures after a meeting with N.R.A.