My guess is fake. It’s too perfect. Why would she have a camera in her office? Why sing to it? And who’d risk losing their job over such a ditz? How come the camera seems to track her for half a second there? Not to mention the laugh - sounds fake.
Yes, she really does take the dive realistically. That’s about the only part that makes me wonder… and the fact that I’ve known obnoxious ditzes like this.