No, the DVR only records actual Xbox One gameplay. I don't know why, but I've seen speculation that the reason you can't just record/broadcast everything that happens on or through the Xbox One is partly due to legal concerns, as it would make pirating copyrighted materials much easier (just think about users broadcasting a movie over Twitch, or DVRing movies/music and uploading to the internet). I'd guess that the other companies that currently allow their content to be broadcast on Xbox One (movie studios, music labels, etc.) might not allow it if the Xbox One suddenly became a popular tool for pirates. Hopefully, though, they figure out a way to make this happen.