No, you’re right. The EC/OC doesn’t have a contractual relationship with the tenants, the landlord does, and the landlord has a legal relationship with the OC.
The EC certainly can’t tell tenants to perform duties, that is just ridiculous. They can’t tell owners to perform duties either, e.g. rubbish, gardening etc. In both cases how they are going to make them comply? A strata plan isn’t a police state.