blockchain without cryptography is like writing a data structure without any motivation for its existenceNote that you said asymmetric cryptography and your parent said that asymmetric cryptography is not the basis of the block chain. And they would be right, at its core, the blockchain consists of blocks of transactions in a Merkle tree. The Merkle tree typically uses a cryptographically strong hash, otherwise it would be possible to modify the Merkle tree without anyone noticing. But a hash is not asymmetric cryptography.
In many applications of the blockchain, asymmetric cryptography is used to sign transactions. But that is largely orthogonal to the blockchain as a data structure. The blockchain as a data structure has useful applications without transaction signing, etc.
What makes the discussion clouded is that some people define 'block chain' as transaction blocks in a Merkle tree, while others also consider distributed consensus, etc. to be part of the block chain.