Council do own the land. Although like with many other private facilities on council lands, the agreement on usage is fairly ironclad between all the parties. Neither council or Eels are breaking it without serious reparations.
The facility however is jointly owned by Parra Leagues, Hills Council, state and federal governments.
If I were to say any one party had the biggest say on the entire centre (land and buildings) being used for what purpose, it’d actually be the state government.
My source? From the mouth of the person who signed the agreement with Hills Council. What’s your source?