Not necessarily is DID connected to publishing something on a blockchain. First: DID does not make any statements to the underlying infrastructure, this can be a completely decentralized public, permissionless blockchain but also public, permissoned ledger(also decentral but a little less) or the did Methods using a central server as referenced in the w3c mozilla response. DID for example solves/enables some aspects of the 10 principles of SSI, e.g. portability