That's right. In the Bitcoin network, there is no need to report double spending or blocks with insufficient proof-of-work. This is because every node in the network has a copy of the blockchain, and they can all see for themselves if a block is invalid. If a node sees a block that is invalid, it will simply reject it and not relay it to other nodes.
This is one of the things that makes Bitcoin so secure. The fact that every node has a copy of the blockchain means that there is no central authority that can censor or manipulate the network. If someone tries to double spend, or if they try to mine a block with insufficient proof-of-work, the other nodes in the network will simply reject their block and continue to follow the valid chain.
This quote from Satoshi Nakamoto is a good example of his foresight and understanding of how Bitcoin would work. He understood that there was no need for a central authority to verify transactions or to prevent double spending. Instead, he designed Bitcoin in such a way that the network itself would be able to do these things.
This is one of the reasons why Bitcoin has been so successful. It is a decentralized system that is secure and reliable. It is a system that is not controlled by any one person or group, and it is a system that is open to everyone.