The post is old but it might be worth to clear this
Those apps are probably using undocumented API. Apple doesn't accept private API when apps are submitted to the app store, however they might not be looking for usage of undocumented notifications
You can find more information in here and here
Those apps show you the download button after you click video, and after the video starts. So probably they are listening for media playback notifications and get the url from MPMoviePlayer instance.
By the way, apple doesn't allow apps that download videos from youtube. There might be some apps on the app store that does that, but I recently got rejected because of this. It might not be worth the hassle, as most big video streaming websites don't want people downloading their videos and work hard to make sure that they don't.