Litter - fatal digestive problems???

OK - from what I have been reading (new cat owner) they say that the clumping litter is bad because when your cat cleans itself it may clean litter off and the clumping agent in the litter getts in their tummies and hardens. OK - what do you guys think? The "Cat's Pride" litter that is non perfume all natural (red package not blue) really doesn't clump at all and doesn't hide the smell - of course I dont' want an overpowering perfume smell either. I don't want to hurt my kitty - I was thinking how about something like fresh step on the bottom (the pee ends up since it doesn't clump) and then non perfume natural stuff on top? That would last a little longer than two days maybe? HELP! Debbie