When law enforcement says she did....she did. Unless the entire police department is on some great big conspiracy because they are out to "get" her. This story is black and white, cut and dry. Law enforcement told the media she admitted lying about the entire incident. Case closed (literally).
Law enforcement is famous for saying one thing, then changing their official comments after a video comes to light showing they had lied, as was the case in Ferguson, Baltimore, New York, etc...
So no, the case is not closed.