Question to the OP: what makes you think that the private key printed on a piece of paper actually corresponds to the address printed next to it? The well-known motto in the bitcoin community states that you shouldn't blindly trust everything you see but verify it for yourself. Have you tried to verify that the private key is real and that you haven't been pranked or tricked into believing that you magically became richer overnight? One of the ways to check the genuineness of a private key is to try to spend coins from the address (transfer them to the wallet you control). Alternatively, if you don't want to get in trouble because of someone accusing you of stealing someone else's property, you can simply sign a message with a paper wallet's address and private key. This way, you will verify that the paper wallet is real and that you're not wasting your time trying to find the owner.

What do you mean by "owning"? How do you claim ownership over random numbers? Don't they belong to the nature of things or the universe we live in? Technically, that you generated some random number doesn't automatically make you a rightful owner of this number but rather its discoverer.