I can see both sides of the argument here, as a reptile owner what is the drama, they are in enclosures and a relatively odor free....however have you walked into most reptile stores...there is a strong odor, this stays in the carpet and the blinds....even after a good clean.
The owner has the right to say no to any animals, even if they are in enclosures.....it is their property after all, by hiding the fact you also open yourself to potential prosecution under the Act as you clearly know that you are not permitted to have them, but have decided to do so anyway.
It could be worse, there are some city councils that are attempting to limit the ownership of reptiles in a similar way to cats and dogs, they will have access to wildlife authority details about reptile ownership and will be able to enforce their regulations.
Be upfront when renting, we were, we had no problems, they asked us to keep the rats outside in the garage and ensure that the house was left in a clean, odor free state when we left, or face paying for replacement of carpets and blinds!! This wasn't a problem as we ensured that all reptiles where kept in rooms with floorboards. No limits were applied to us, they also stated that if we did not tell them upfront then they would not have approved it later on!