No that’s not correct. If there is no by-law (exclusive use) then by default the Owners Corporation is responsible, refer sections 62 and 54. The reference you are looking at may be to the note to section 62 which provides that a decision under s 62(3) can be reviewed by an adjudicator.
https://www.austlii.edu.au/au/legis/nsw/consol_act/ssma1996242/s54.html
https://www.austlii.edu.au/au/legis/nsw/consol_act/ssma1996242/s62.html