HDB’s reading is faulty and exposes a poor understanding of cats (and dogs). Cats can easily be kept in apartments for the precise reason that they don’t need to be taken out to pee/poo or exercise.
If this is the reasoning they use, then it is actually dogs of all kinds that should be banned from HDB flats. They actually need to be taken out of the flat regularly. Cats can be kept entirely in an apartment.
Dogs shed as much as cats too. There is no reason for cats to be banned from HDB flats.