Just to totally confuse you, I'm going to give you three possibilities (because without knowing your cat, there's no way I can give you a specific diagnosis for his behavior). Here they are:
1. It may just be that he dislikes the litter substrate. Try putting a second box out with a different type. See which one he chooses. Since he covers when the litter is clean, you may need to have a second box entirely.
2. He just may not like the idea of another cat's scent in there. In the wild, a more dominant cat may leave his waste in full view of other cats just as a reminder that he's king of the hill. Sometimes indoor cats can get into that behavior as well.
3. Finally, not every cat reads the instruction book on how to conduct business in the litter box. Many cats just don't cover.
More cat-care and behavior solutions: