> The contract you sign with the carrier says you don't own the phone until after the contract period expires

You mean like when you sign a mortgage to buy a new home? Only it isn't true. You own your house even if you default which is why you can rip all of the copper and sell it for money before they foreclose on your home.

The contract with the carrier definitely doesn't say they own your phone. It makes no sense for them to say that since they have you for early termination fees.