I wonder if anyone has watched a cats' stance while urinating/defecating. A cat (at least all of mine) while urinating will have it's bottom very close to the litter. A cat while defecating will use many different stances. None use the same stance as they do while urinating. If they squat (very few do) their legs are drawn further forward to facilitate the easier release of the waste. If they do a half stand their legs are very stiff. Quite a number of mine stand with their front paws on the side of their box while their back legs are fully extended. I watched one yesterday balance precariously on the edges of two boxes that are close together.
My point being I do not feel a cat should be using a toilet meant for an animal who sits to do their business. Pretty simple. Humans do not use different stances. We use one. With our butts planted firmly on the toilet.
As for her being an illegal - do you own or rent the condo? If you own how can anyone justify what you can have in your own home? I am sure if you check you will find a few other "illegals" around. If your cat is using the floor to do half of her business I can guarantee you over time that floor will start smelling. It won't matter what you use to clean it. It will smell.
There are many good litters out there that can be flushed. They are Shweat Scoop, a wheat based litter; Feline Pine, a pine based litter; and many others. Please do not use a clay based litter as that is not safe to flush. As Love4Himies said, you can bring in a bag of litter disguised as many different things. That's what shopping bags are made for. A litter box can be a storage box. In fact often storage boxes work much better than a litter box because of the increased size. It gives the cat the luxury of moving around in the box to find the "perfect spot". Oh yes, cats do that too.
What you are missing is that a toilet is not a comfortable place for a cat to do its' business. The best way to tackle it is to give in and buy a litter box. They can be kept meticulously clean and the evidence flushed so no odour escapes to give away your alien.
Assumptions do nothing but make an ass out of u and me.
We can stick our heads in the sand for only so long before it starts choking us. Face it folks. The pet population is bad ALL OVER THE WORLD!