I haven't seen the movie yet but it seems like they're just randomly throwing elements of Star Trek into the new movies without understanding their context in an attempt to make it a Star Trek movie. Section 31 was always out of place in the utopian future of Star Trek and I think it's a mistake to use it outside of the morally ambiguous setting of DS9.
It makes sense if you consider Section 31 an organization out to only protect the interests of Earth. Think about it? In DS9 and ENT we've only known Section 31 members to be human. The fact that they are in the "Earth" Starfleet Charter before the Federation was founded means that throughout history they've always been there. DS9 put a name on such an organization but with how easily and mysteriously Sloan was able to slip in and out of DS9. It's not impossible to think this organization uses not just methods, but technology that Starfleet legally agrees not to use. Cloaking devices etc.
Morals in Starfleet havent't always been clear cut things. Look at the war nearly started in TUC, phasing cloak from TNG Pegasus, the theft of a Romulan cloaking device by invasion of the neutral zone by Kirk and Spock, and of course the virus used on the Founders. Starfleet Command/Admiralty was either behind or had a hand in everyone of those incidents. Unless caught red handed, holding a smoking gun in view of others. The perpetrators (Starfleet Comm) rarely face repercussions.
In this new timeline, the pollution of history with technology 125 years from the future can change the balance of power. Klingons had 25 years to study the Narada, while Starfleet only had censor scans to go by. I haven't seen the movie yet but from the spoilers. Section 31 being so casually name dropped seems that earth is still in a heightened state of security. The Nero incident was only 1 year ago by Into Darkness canon. Like America's terror threat level system.