I think he means odorless in the same way I'd call my husky odorless--their fur doesn't hold odor like say, a lab. Even if my dog has been rolling in mud and other crap all day, once he dries off (and cleans himself up, like a cat almost) he has a very mild smell.
Obviously not odorless, but clean? Seldomly needs bathing?
If you dislike someone, walk a mile in their shoes. Then, you are a mile away from them, and you have their shoes. --Jack Handy