See, you backtracked. technically yes, and strongly implied are not the same thing, which was what I joking on you about.
And your example doesn't work. Saying one is a cake eater does not imply or denote exclusivity, therefore, anyone who eats cake or has eaten cake can be fairly described as a "cake eater" where-as, a murderer denotes someone who has murdered and not someone who CAN murder, which denotes ability. It's like the square rectangle arguement. All squares are rectangles but not every rectangle is a square.