IF the legit owner still has a copy of the Private Key of the paper wallet, (s)he can easily prove ownership by signing a message with the particular Private Key. I wrote that before already.
If they had the private key to that paper wallet they no longer need to prove ownership, they would just move the coins 
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The owner of the Private Key of the address that funded the paper wallet, ie. the address from where coins were sent to the paper wallet address, must not necessarily be the owner of the paper wallet. She or he can be.
That's right but at least there is a link that can be pursued to find the real owner.