NFT's: Copy and paste an image and then re-mint that image as your own NFT

Hi Eth community,

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I've been doing some thinking and came across a conundrum that I'm sure is accounted for, so I'm here searching answers:

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Lets say Snoop Dogg trades me his Punk #3831. I now own the NFT for this punk. Now I parade it around as my display picture on Twitter and someone right clicks and saves it. They then take the image over to an NFT minting platform, and create an NFT with the saved image.

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This scoundrel jacked my image, and created their own NFT with it. Now say we have games where we can take our NFT and use them as our avatar. How would that game refute their NFT and declare mine the true Punk #3831?

Could we both be on there with the exact same pixel makeup, but different NFT's? Where in all of this does verification happen?

Thanks