I don't know. It is against YouTube's ToS, and the owner's copyright, but the app isn't for YouTube, it's just for videos in general.
If I download Flickr photos with the built in "save image" feature, then I'm violating Flickr's ToS, and the owner's copyright, but it doesn't make the save image feature a bad thing.
iCab Mobile had to remove the YouTube download function with the latest update:
Apple rejected the update. The reason was not the bugfix, they rejected the App because of a feature that was available for years in iCab Mobile and which is also available in hundreds of other Apps in the AppStore. They rejected the App because it is able to download videos from YouTube so you can watch the videos offline.
This really bad for the developer as he is on his blog apologizing for the loss of a feature. Apparently it is only disabled for YouTube, whose ToS Apple has to respect. Guess I won't be upgrading cause it is so useful to download on wifi rather than burn mobile data. Also videos disappear never to be seen again.
There already was an instapaper for video. It was called Spool. First, Google asked them to not download YouTube videos, then Facebook acquired the company and they shut down.
f* the download restriction...there are tons of apps out there with this function, and i guess google has to put these lines in there rules.