I am only guessing as to the earlier poster's intent. But, I took the earlier comment to be about distributed system application architecture. The statements make some sense to me if implicitly considering boundaries between the application and DB query engine, rather than the internal elements of the query engine itself.

Through this lens, a pull-based architecture is your conventional N-tier application where the stateless application issues queries and consumes results. The individual consumer (and producer) agents are independent and decoupled, allowed to handle failures with simple restart/retry while in control of their own transactions.

Conversely, a push-based architecture is often rendered into some enterprise message bus with queues and brokers. The applications can only subscribe to the queues and pub/sub system, but lack any real control fault recovery or transactional boundaries.