The thing is, Trump himself is responsible for Cohen turning on him. After those tapes were released Trump went off on Cohen over twitter. It was after that Cohen decided to cooperate with Mueller. If Cohen is a threat to Trump and that is why they are saying this idiotic crap, then it was a self-inflicted wound anyway. A consequence of the fact that Trump can't control himself.
It happened before that. It happened when Trump said "I always liked Michael" which was basically a kiss off. So of course he rolled over after his lawyers talked with the prosecutors because they had him by the balls. It's the smart answer, the best way to cut his losses because he knew he couldn't depend on executive clemency. He's kinda the John Dean of Stupid Watergate.