You're making the same mistake a lot of CRIDers do - forgetting that we are social animals, and part of the environment we adapt to is other people.
The strongest, least inhibited man, in isolation, is nothing compared to organized society.
"United we stand, divided we fall"
Think of a tribe of egocentric liars, and another tribe of people who cooperate with each other. The cooperators will win the war between them; it's happened many times in history.
In summary, "fittest" for human beings includes the ability to cooperate with others.
When I posted about the Constitution and Bible above, I mentioned that murder, theft, etc are illegal under all systems; they all condemn lying as well.
Well, not all systems condemn lying. Creation/IDism and socialism all support lying for the "greater good".