Hi Tamara,
Unfortunately this is correct. The bathtub is considered to be lot property as it is deemed to be within the airspace of the lot.
While the building was a refurbished building the developer/builder would still have an obligation to provide home owners warranty on the works done by them in renovating the building. Owners are able to claim under the HOW scheme for building defects within 7 years against the builder, but this gets complicated.
Good luck.
Mr S