[charcircuit]

>Does YT own the content?

No, they don't.

>He is downloading a video made by another user

Without a license from that user to make a copy of their video.

[krageon]

There is a copy of the video on your device every time you watch it.

[gnuj3]

Yeah, if that other user copyrighted the video.

[charcircuit]

Works are automatically copyrighted when they are created