Hmh? You seem awfully uptight about our TOS hero and his supposed honor. Why the deadly serious attitude?
The thing about Kirk is that he is not a modern hero. He is a cluster of cliches from half a century back, relying on morals deriving from the preceding centuries. Positing morals and attitudes on this caricature is like shooting fish in a barrel, and sometimes great fun.
Sectopm 31 is made up of like-minded Starfleet officers who otherwise have their regular assignments like everyone else. Their exploration missions are no different than any other starship, they're just a lot more interested in results that have tactical value than other commanders might be.
It appears that S31 in ST:ID is a somewhat more "open" organization than in DS9, then. Fair enough. This does mean that the Starfleet of the movie isn't much different from the Starfleet of TOS, as its policies bring a starship to the same spatial backwater to meet Khan.