Except that's literally what they do, using a combination of digital signatures and timestamp. You can have a copy of the same NFT even on a different chain but the timestamp will be higher, therefore proving it's not the original.
Plus the problem of referencing the content is solved by having all data on chain (likely on layer 2). Recurring problems in the world of art trade such as provenance, certification etc. are elegantly solved by NFTs.
> someone copied and pasted this guy’s real-life artwork, created an NFT out of it
Ironically that's exactly because the artwork was not (referenced) on chain. If that was the case any subsequent copy would not be recognized as the original because of the timestamp and wouldn't have nearly the same value. That's why a simple digital signature scheme based on something like Keybase wouldn't work.
I understand and appreciate the author's skepticism but, IMHO, he did end up looking like David Letterman in that video.