My sister had a black lab that emptied the litter box pretty regularly--she would come out of the bedroom with litter stuck to her muzzle and licking her chops and act as if she hadn't be doing anything at all!
Oh yeah, our dog loves it and always has, no matter what her diet is like. Funny thing though is she hates cats and goes berserk if she sees one or even hears us say the word cat. So we aren't getting another one (ours died a couple years ago). If she were smarter, she would start getting along with cats so we could get one and then she would have her favorite snack right here in the house.
Cat food has so much protein that most of it goes right through them, so dogs often eat cat poop. It's pretty common. Pretty gross, too. (But then, dogs can be pretty gross, bless them.) No solutions for you, sorry.