I can see both sides of the argument because the lines are definitely blurred in terms of jurisdiction, who works for what agency in what capacity, etc. That being said, <PERSON> doesn't condone murder / deadly violence / capital punishment in any shape or form.
This is the rift between <PERSON> and the Elite: He holds life to be sacred, they do not. He believes no one has the Authority (COUGH) to take a life, even to save another (or many others).
The jurisdiction argument is interesting, but doesn't hold weight after thinking about how many times <PERSON> has gone after the President of many countries, including the US, to put a stop to bloodshed. Even when a <PERSON> is driven to kill (no spoilers, but JLA has tackled this), and we eventually see our <PERSON> driven to the same extreme, our <PERSON> always finds another way beyond killing.
To my knowledge, that's the only ideal that <PERSON> never deviates from, and cannot deviate from, lest he lose his identity altogether (and easily become like <PERSON>, or <PERSON>, or even <PERSON>).
As for why he took it upon himself to stop <PERSON> and the Elite, for the same reason he stops anyone causing death and destruction, even in the name of justice: Earth is his home and he has vowed to protect its people, even peices of crap like <PERSON>.
EDIT:
This question reminded me how good this movie was, especially the ending, so I was inspired to rewatch it. 80
Just to directly address the jurisdiction issue, I noticed in the beginning that when <PERSON> tells <PERSON> his team's supposed origin stories, he says:
...after that, it's the usual fishtale: Her Majesty's Secret Service took notice, gave me a bed, and taught me a thing or two about hurtin' bad people in the name of freedom. I met this lot [gesturing to his team] during a particularly disenfranchising tour in Africa, and we decided to make a go of it freelance, like yourself. The rest is current events.
Later, when <PERSON> tries to publish the truth about the Elite, she says <PERSON> was shut down by British Intelligence before the story left his computer. She also implies that it was done to conceal the fact that British Intelligence trained <PERSON>, but it could be interpreted that they are still covertly active agents.
I personally believe they're freelance though, since they're never seen reporting to anyone, or discussing any kind of orders. 600