Well, UltimateCharlieSheen, The Rhino was all over the news, and I'm pretty sure Stark had time between getting bevied to put on the old armor. He's a good guy, really. Besides, one of the main reasons behind The Ultimates was to make the public feel like there was a super-human team to defend them from super-human bad guys and, since The Rhino's attack was a very public thing, The Ultimates had to be involved at some level. And the submarine thing, well, that's just the right thing to do when it is expected that nobody else would be able to do it, right? They are superheroes after all.
And as for The Ultimates only dealing with the big threats, they are there to deal with all sorts of criminal activities but essentially those that cannot be dealt with by the "normal" authorities. I'm sure SHIELD and The Ultimates would be very interested and involved if a guy with four mechanical octopus arms was running around killing folk, but they wouldn't be needed if Spider-Man dealt with it first. Or in the case of some kind of mutant threat, they wouldn't be needed if The X-Men dealt with the situation first. Just like they wouldn't be needed if an alien race was attempting to overtake the planet, if somebody dealt with it first. But who can deal with an alien invasion before The Ultimates? Nobody. Besides, how interesting can a story be with Captain America, Iron Man, Thor, Hawkeye, The Black Widow, The Wasp, Quicksilver, and The Scarlet Witch all piling on top of Doc Ock or Mister Sinister? And in the case of a supposed member of this government super team going nuts (ala The Hulk, and soon-to-be Thor), then it would be up to the team to bring them down to save face and try to keep the public on their side.
That's the way I see The Ultimates' role: dealing with very public situations and situation that involve the image of SHIELD.
STRIKE is the British division/equivalent of SHIELD.