Fake means the seller/creator of the NFT didn't own the content in the NFT.
If you use an image/music/book that someone has got a legal trade mark/copyright on and you reproduce it you are breaking their copyright. Copy a photo and change a pixel, or change a small part of a music track or a few words in a book and reproduce (in an NFT or not) you're breaking their copyright - selling a fake and likely will be sued.
It would be interesting if the NFT didn't contain or point to a copy of the original content (picture, tweet etc.) but just included its name (an NFT of "The first Jack Dorsey Tweet").