Also, what did he expect would happen if he made that particular part of their conversation public? No, he's got a mental deficit of some kind.
Maybe he figured out a way to destroy Rosie simply by telling the media about Barbara's conversation with him. He knew ahead of time that Barbara would have to publicly deny she'd ever said anything of the sort to Donald. He knew Barbara wasn't going to admit anything. And when Rosie and Barbara met up again after their vacations, Rosie lit her up. And with Rosie yelling profanities at Barbara, Rosie is self destructing just as the Donald predicted.