That simply isn't true. People do have some rights over copyrighted content, it's called fair use.
I think there is something that is left out of these arguments...er, discussions. There is one significant legal difference between buying music on a CD and purchasing via iTunes (and I assume other legal download services) that people conveniently forget. None of my CDs came with a legal agreement or explicit statement of how I would or would not use the CD. There are implicit understandings based on copyright laws and fair use that govern what I do with the CD. And you are all basing your arguments on that model.
In contrast, your iTunes purchases do come with a legal agreement. You agreed to it when you installed iTunes, and you confirm your agreement with every iTunes update you install, and you agreed to it when you created you iTunes account. Most of you probably just clicked OK and proceeded to use iTunes without actually reading the document. But it is a legal document, and you agreed to it. And like any legal agreement, you can in fact agree to give up certain rights. It's very similar to software license agreements that state you can only the software on a certain number of computers, etc, etc. The iTunes agreement has additional terms outlining how you can use iTunes purchases. The latest version has terms for your use of movie rentals. Here's one particular line that you agreed to:
"Your use of any Products purchased or rented (as applicable) from the iTunes Store is conditioned upon your prior acceptance of the Terms of Service, including, without limitation, the Usage Rules set forth therein." [my emphasis on "Usage Rules"]
http://www.apple.com/legal/sla/
Fair use is still a powerful legal argument (I hesitate to call it a "right"), but like it or not your acceptance of the iTunes service agreement will limit, to some degree, what you can do under fair use.