Yes, you can sign it with your own private key because you are now the "creator".

That's the point of digital assets, they are fungible by definition because it's a bunch of 1s and 0s, doesn't matter which system you run it on you will get an indistinguishable output.

Yet two fully bit-by-bit identical digital assets can have very different social and monetary value based on who stamped their name on it.

Of course for that to work you need an easy way to check who owns a particular wallet so you can verify they did actually stamp their name on it. And quite a lot of NFTs exist without this level of proof hence rampant fraud.

Except the world knows who the creator is and your 1s and 0s aint it