ummm...for those of you thinking you can have the video because no one registered a copyright for it, you're wrong.
without going too deeply into a complicated legal discussion (because i am realistic and know none of you really cares

) the current version of US copyright law allows the copyright protections to attach
automatically when the work is created.
only certain types of works qualify, they need to be "original" and in some some type of "fixed medium" - i.e. a written document, a tape recording, a photo, etc. This video definitely is "original" enough to qualify. (I probably can't copyright a blank piece of white paper or the alphabet typed in 12 point times new roman, it's not original enough).
OK, so the video is original. It's automatically entitled to copyright protection by the "author" - whoever directed the video or controlled its direction (here, either Rick or Paris), or whoever now owns the copyright (if it was sold). The only thing that registration does that's relevant here is gives the US govt an official record of your "work" so they know what you're trying to protect. (There are other issues relevant to burdens of proof required if you pursue litigation, but I'm not going to discuss it here.)
Owning a "copyright" means what it sounds like - you have a "right to copy" the work and prevent others from copying. There are some exceptions, like parodies and what's called "fair use," which allows limited use of copyrighted works for certain purposes that society feels are beneficial (i.e. educational and charitable purposes). Whether or not the alleged copyright infringer is selling the product or otherwise commercially benefitting is not really relevant in determining if they violated the copyright (it does affect damages, i.e., how BAD was this conduct?)
So if Rick or maybe Paris decides to assert their copyright in the video, they could theoretically sue every website hosting the video and everyone downloading it (if they could find them). It's similar to the Napster lawsuit and the latest RIAA suits against KaZaa users.