Exactly, that’s why Blockchain is not a solution to every problem, like shitcoiners want to make it seem. But in Bitcoins case all information that is necessary to verify the information exists inside the system itself. It’s based on digital signatures. For a transaction:

• You need a hash of the previous transaction(this shows how you got the coins).
• You need the public key of the next person you want to transfer it to.
• A digital signature of the two previous points, which proves you’re the owner of the coins, this can’t be faked it needs your private key, you can only have the correct private key if you were the previous owner of the coins. That’s why you need to secure your private keys, because it serves as a proof of ownership.

It’s impossible to even transact with false information like this. You can’t try to spend other peoples coins or spend coins you don’t have, or write any bs information you want inside the Bitcoin Blockchain. So then only the double spend problems remained, but full nodes/ miners validate new transactions before they get taken into a Block. Only utxos can be spent. Invalid blocks are rejected. Only objectively valid transactions are taken into new blocks. When there’s conflicting transactions the one broadcasted first is considered valid. For this you have a timestamp server that relies on PoW. This was the first time this problem was solved in a decentralized, trustless way, Bitcoins validity is ensured objectively.

When there’s the nft bs and other things that shitcoiners want to sell as solutions, then blockchain isn’t the solution. As it can’t verify information that is outside the system. Like art, real estate, medical records etc. As you can simply add in false information and there’s no fully objective way of verifying it. And like you rightly stated it doesn’t matter if false information can’t be changed, but on centralized blockchains not even that is certain. So there a blockchain wouldn’t be different from a centralized database as both need trust to work.