So anyway, not that this is even one of the important issues, but the way to sort out who is lying (the most)...
Simply: Nixon claims the girl has a video of him in his underwear, which she stole from his phone while left in his office for 20 mins months ago, whilst he was talking to police.
If this is true, he will have the video on his phone.
If he is not in possession of the video himself, then he is lying.
If he does have the video, it proves she was lying, because she'd have had to film it on her own phone or camera, so he wouldn't have access to it.