Not true. Someone could take an image that I've created, stick it on a server, create an NFT with a URL pointing at it, then sell it. Likewise, others, including me, could then create an NFT with a URL that points at that piece of data. The original creator (me in this situation) wouldn't have created the 'original' NFT.

Right, just like how you can make a deed that says you own 30 Rockefeller Plaza.

NFTs don't solve counterfeiting when anybody can create a 'counterfeit' at any time.

never claimed it did, only that NFTs can potentially provide a better way to assign/transfer copyrights than the current system of paper contracts.