An example would be that I, as the central entity, know which public keys/key pairs I want to trust, and the proof of work is the owner of said key signing a given block with it. So as the central authority I can't unilaterally rewrite history, but I can unilaterally decide whether the chain is valid.
E.g. Alice wants to deliver a package to Dan by means of Bob and Carlos as couriers. So Alice signs the initial block using her public key and gives the package+signed block to Bob, who signs and gives to Carlos, who signs and gives the package to Dan. Dan can independently verify his trust in Alice, Bob, and Carlos's public keys and then be sure that the package was passed along in the manner recorded in the blockchain.