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, Superman doesn't condone murder / deadly violence / capital punishment in any shape or form.
This is the rift between Supes 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 Supes has gone after the President of many countries, including the US, to put a stop to bloodshed. Even when a Superman is driven to kill (no spoilers, but JLA has tackled this), and we eventually see our Superman driven to the same extreme, our Supes always finds another way beyond killing.
To my knowledge, that's the only ideal that Superman never deviates from, and cannot deviate from, lest he lose his identity altogether (and easily become like Black, or Lex, or even Doomsday).
As for why he took it upon himself to stop Black 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 Atomic Skull.
EDIT:
This question reminded me how good this movie was, especially the ending, so I was inspired to rewatch it. Just to directly address the jurisdiction issue, I noticed in the beginning that when Black tells Superman 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 Lois tries to publish the truth about the Elite, she says Perry 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 Black, 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.
