Why you can't just screenshot an NFT

This was really cool and answered one of my main questions. There are many blockchains, any of which could host an NFT (even the same NFT). Who decides which entry on which blockchain is the "authentic" one? This video's answer is "it's decided basically by whichever one is the de-facto popular choice". That works well enough I guess, as long as there really is one clear choice and it isn't later overtaken by a rival. The problem is that it's a marketplace, so it seems it's only a matter of time. Now, my understanding here is almost certainly still missing a lot of details, so I'd appreciate if someone can help explain why it's not the wild west and why the rich and powerful can't just sponsor and promote another blockchain to the top...

My other question that wasn't covered here directly is, what if you change it a bit? I guess this question could also apply to existing forms of art but digital obviously makes the copying much easier (and yes I'm aware many modern images are digital and we've solved copyright long before blockchains came along). But with an NFT, if you change some pixels, the hash won't match. So how do you prove ownership when a single pixel change could prevent almost any algorithm from identifying it as the "same image". And if we relax the algorithms to catch such frauds, how far can the algorithm be relaxed before it misidentifies completely unique works as a copy?

I'm actually onboard with blockchain tech in general (I've even coded my own) but NFTs are something I haven't wrapped my head around yet.