Greengrass, meanwhile, is also clear on what Damon brings to his films: a quiet, stabilizing decency.
"He's a brilliant character actor. He's a brilliant physical actor, which is pretty rare. He brings a core of integrity to the heart of the film, which is important when you're exploring events like this," Greengrass says.
He says Damon is equally decent in real life.
Damon will banter about the future of the news business, his reasons for marrying his wife in an impromptu city hall ceremony after word leaked about their original planned nuptials, and his favorite Manhattan sushi haunts just as easily as he'll debate Middle East politics.
With Damon, Greengrass says, "what you see is what you get. He genuinely is nice and incredibly hardworking. In all the years we've made films, I've never once seen him be crabby and anything less than 100% enthusiastic. He's immensely popular amongst crew and cast."
He and his family — Lucy, stepdaughter Alexia, 11, and daughters Isabella, 3, and Gia, 1 — are now settled in Manhattan.
"They're all thriving. That's why we're so excited about it here," he says. "We're not leaving. Nobody bothers me. The younger ones are not aware of any of the celebrity (stuff). We walk to school every morning. We play in the park. It feels like a normal life."
As with many who juggle parenting and a career, he recalls the moment he decided working might be less challenging than being at home 24/7.
"It was really nice to be at home. It's funny. People think of it as slowing down, but it's not that way at all, because there's so much going on in our house, with three kids, cousins and friends coming over. It's pretty hectic," he says.
On the surface, Damon appears to be leading, if not the perfect life, something that comes fairly close.
"I hope so," he says, knocking on the wooden table in front of him.
"It comes down to hard work and luck. I've worked really hard, but a lot of my friends have worked hard, too. A lot of it has to be attributed to luck. But it's like anything. Things will always look different from the outside.
I don't think anybody feels they're leading a charmed life, but I certainly don't have anything to grouse about. I do wake up feeling incredibly lucky every day to have the family I have, above all else.
"And kids are kids. They don't care about what other people think about you, it's all about you and them and that interaction. You can't fake your way through that.
"It means sleepless nights, and all of those things are wonderful. I guess celebrity doesn't give you a pass with the real world."
When did you shoot?
Two weeks ago. Sting was our first and Matt Damon was our last. We shot Matt on Saturday and we were very happy that he was game because he was a perfect button on the skit. That laugh was maniacal! He had to present the next day at the Oscars, so I was really hoping he had a voice for that.
San Francisco Gate
It's a tribute to Matt Damon's special quality as an actor - not his star wattage, but his ability to project a certain simple human decency - that we care about him even when we only see the side of his head, the back of his head and the stray glimpse of his head bobbing into and out of the frame. In the first 10 minutes of "Green Zone," it becomes exhausting (for some it will be dizzying) trying to penetrate the loony camera work just to locate the actors and the story.
Damon, whose wholesome, muscular good looks make him an ideal all-American hero-next-door, has done some outstanding character work in recent months (to behold him in "The Informant!" is akin to watching Brad Pitt turn into Philip Seymour Hoffman). But in "Green Zone," he takes back the mantle of leading man with a vengeance, his character barking out hoarse orders to his adoring subordinates and fixing interlocutors with a fierce, sky-blue gaze before deciding whether to trust them (he always makes the right call).
Damon is divine as Miller. His endearingly torn and curious character provides a logical connection with those feelings of dissonance and distress that viewers often encounter when addressing the decision to engage in such an inconsistent conflict. Through this bold figurehead Damon communicates a politically charged message that provides an inside look on the occupation of Iraq.
Grounding it all is the ever-impressive Damon. Firmly established as the action man for generation Y, Damon delivers a tightly wound study of bruised loyalty that honours the American movie tradition where morally driven renegades make the best heroes.
Evening Standard review
Paul Greengrass has directed a film that does what countless newspaper articles, memoirs, government statements and public inquiries have failed to do when it comes to the war in Iraq: exposed the terrible lies that stood behind the decision of the US and Britain to prosecute the war, and it does so in a way that is dramatically brilliant, morally complex and relentlessly thrilling.
But Greengrass must be singled out; with this film he has leapt into pole position as a British director with matchless resources. I could devote the rest of the day to talking about his style: the hand-held, rapid, exciting nature of his shots, the wonderful, breakneck smartness of his editing, but what now distinguishes Greengrass is his ethical curiosity. Whether thinking about Stephen Lawrence or Bloody Sunday, 9/11 or the real reasons for the conflict in Iraq, Greengrass is unswerving both in his manner of observing truth and of unearthing corruption. In Green Zone, he doesn’t put a foot wrong and he has made a film that will not only enrich people and thrill them but one that will contribute something permanent towards correcting the public record.
It is often assumed that war films don’t work at the box office nowadays. Certainly, when compared to Avatar, the film that won last week’s Oscar for Best Film, The Hurt Locker, has made no money at all. But where such films don’t make enough money they might do something better — they might make a difference. I can’t believe people will not go to see Green Zone in their droves. I certainly hope they do, for it is a shocking, replenishing film, not to be missed.
You're part English, Scottish and Finnish – which place haven't you been to?
Finland. All the travel I do is work-related – I have to get a job in Finland. Then I’ll go for an extended period of time. But to just go with little kids… it’s a big trip and tough to try to impose that on them.
Anywhere else you want to go?
I’ve done three or four movies in Morocco and still haven’t been to Marrakesh. I’m dying to get there.
What do you do when you're not working?
We’re a tight-knit family so it’s nice to wind down and read stories, sit and colour and play with Play-Doh. Just relax.
You turn 40 this year but look ten years younger. What's your secret?
Red wine. That, and the facelifts. I’ve only had five or six of those. And I quit smoking five-and-a-half years ago. But, you know, I’ve always had a babyface. I remember having a beer with Tommy Lee Jones in 1994 and thinking: 'God, when am I going to get a face like that?'