Does Airplay on the Apple TV keep a history?

Say I stream a video from a website using Safari on my iPhone to my Apple TV via Airplay- does the Apple TV store the URL of that video in a history somewhere?

Does the Apple TV even retain a history that I streamed the video, or streamed anything at all?

Or is streaming music/video from my iPhone to an Apple TV using Airplay totally incognito?

I ask because I run across a lot of videos I'd like to share with my girlfriend (gametrailers, ted talks, etc), and it'd be easier if she could just pull them up straight from the AppleTV. .

Thanks!