This is an interesting topic. I especially like the boyfriend observation that maybe Twinkie is afraid of predators. I would guess this is behind the natural instict of covering up the waste.
Perhaps the cats we traditionally think of as stinky just feel quite safe and confident.
An alternative thought is that maybe she doesn't really like the way the litter feels on her paw. She would rather leave her mess uncovered. Have you tried different types of litter to see if this helps? The clay-based litter sticks to the kitty's paws if their paws are wet w/ urine. There have been reports of cats getting sick, sometimes ending in the hospital w/ these huge bezoars of litter in their stomachs from cleaning it off their paws. It expands when swallowed or something. If she covered it well in the past, cleaned the litter stuck to her foot, then got sick on her stomach, she might have learned to avoid touching it afterwards.
I have a messy boy, Cooper, who rarely covers also. I feel like it has to do w/ how soon he was taken from his mother, or rather, his mother was taken from him by a car on the freeway where he was found. I think the mothers will usually teach this to the kittens who don't seem to get it from instinct alone. My other cat used to watch Cooper go and then get in and cover it for him. He finally gave up on the lesson I think.
The Littermaid might be your answer because it will scoop it up immediately, eliminating the need for your cat to worry about covering it anyway. It's a pain to clean though when it is time to disinfect it. You have to get a screwdriver and take off the raking part and it's a big mess. I have one out in the garage I quit using for this reason.