Really?
Probably almost every video on Youtube is owned by the video creator. When you upload a video to Youtube, you still own the video and you're granting Youtube a revocable license to use it (see section 6 of the Youtube EULA, https://www.youtube.com/static?gl=US&template=terms). In addition, Youtube enters commercial licensing agreements for much free and paid content.
Youtube videos aren't public domain just because they're on the Internet! No, you can't copy and host data you don't have the license to. And recall that these videos belong to little guys as well as big ones.