That doesn't mean that there isn't a contract between HBO and Warner Studios involved for this, as crazy as it sounds. It doesn't mean that there definitively is one, either -- but depending on how the different divisions are structured, HBO may well be paying Warner for the streaming rights.

My impression is that this sort of deal -- where the production arm may well shop around a product to different networks/services, even if the parent company actually owns one -- is becoming less common as nearly everyone's starting their own streaming service, but AFAIK it still happens, particularly for movies.