OpenSea is very nearly "entirely on-chain" if I'm understanding your point correctly. It's powered by smart contracts. It's not custodial like Coinbase or Robinhood. Users custody their assets in their own wallets. They trade by submitting transactions directly from their wallet to a smart contract address on-chain which facilitates fulfillment of the trade. The code for these smart contracts is open source and verifiable.
It may not be obvious to more casual observers, but there is a lot of trading volume happening on on-chain exchanges these days (as in easily 10B+ in trading volume per day with most of this coming from futures).
Anyone can generate an NFT, including IP you don't own or existing collections.
Hundreds of wallets might contain a the same monkey picture (or same hash and IPFS link to nitpick).
What matters is that Opensea says you have the "real" one.
Their database is the real list of who owns what, the blockchain is a distraction.
You can see it in their anti-theft systems. NFTs get hidden and blocked from trading after a police report, even if it's still there on the chain.
I would disagree with that characterization. There are dozens of NFT marketplaces which all have access to the same underlying data. An NFT is denoted by its address on chain, which is trivial to find. Similarly anyone can create a website that looks like Google, but the "real" google is the DNS entry at "google.com".