It's always been important for Greengrass to shoot in real places: Captain Phillips has a strong environmental sense. He felt getting the right ships - a container ship, a US Navy ship, skiffs and the lifeboat - was key.
"They were incredibly claustrophobic, and that created the compression and the drama that really drives the story.
"If you can create a desperate urgency on a film set that's real, everyone inhabits a frenzy of chaos, it can be a good thing because what happens is everyone starts to inhabit the world of sheer terror, in a good way."
The film delivers one of Hanks' best performances in years and Greengrass is similarly enthusiastic about Barkhad Abdi, who plays the chief Somali pirate, Muse. "There's a great challenge in this film, which is: how do you present young men who are intent on violence and mayhem, kidnap, and piracy? You don't sentimentalise, the clear moral essence is dark and dangerous. And yet you find, by degrees, the humanity of that, so you get a portrait of complexity and humanity."
The film plays out as a battle of wills between Phillips and Muse as the cameras whirl about them, while also capturing the clock-ticking urgency of the US Navy rescue mission.
Popularising the groundbreaking shaky-cam style on his two Bourne movies took negotiation, says Greengrass.
"I remember the first hour of rushes hearing people of authority behind me whose names I won't mention, going 'What the f***? what the f***? Why does he have to do that!?"'
But he says Hollywood was very good to him when he explained himself. "The idea that they sit around trying to find ways of interfering with directors' work is so wide off the mark. When that film started to work they realised that their movie audiences were much more conversant with those images than they knew."
Greengrass got his passport to Hollywood with Bloody Sunday, the gritty docudrama about the British Army's killing of 13 peaceful protesters at a march in Derry in Northern Ireland in 1972.
With the Bourne films, Greengrass wanted to bring his visceral style to commercial movies, and make some good money, too. "I had a particular view about what an image was cinematically, it was very fluid, very kinetic, very raw, very rough."
With the 9/11 film United 93, Greengrass recreated the story of the 40 passengers on that United Airlines flight in 2001 who, hearing of aircraft crashing into Manhattan and Washington, fought back against the four Islamist terrorists who'd taken over the plane.
There's a similar sense of solidarity against the odds among the crew of the Alabama in Captain Phillips.
"Richard Phillips was in command of a crew of some 25 men. Richard Phillips' experience was the worst because he was taken off the ship and into the lifeboat.
"One of the things I'm most proud of in the film is that you sense that crew moving together as one."
It's a movie like all Greengrass movies, fiction or non-fiction, that manages to combine edge-of-the-seat tension with a political brain.
As Greengrass told the Independent: "Film-making is about having a point of view. And that needs to be something authentic to you. If you can find the stories or characters that enable you to express what is truly inside you, then you can try to shape the film according to that."
TOM HANKS ON THE REAL CAPTAIN RICHARD PHILLIPS
"I read his book, actually, prior to reading the screenplay. You have to load it up with an awful lot of facts, quite frankly. You've got to read, look at video, and listen to stuff, but there's always some sort of detail that makes the final tumbler lock into place. I drove up to talk to Rich and Andrea on a couple of occasions.
"You don't want to be an idiot, you don't want to ask: 'What was it like? What were you feeling? Are you a hero?' You don't ask questions like most journalists do. Andrea said something that was interesting. I said, 'Did you ever visit Richard on the ships?' and she said, 'I used to but it's no fun because Richard's a completely different human being when he's on board, when he's on the job. He's very easy going, I would describe him as happy-go-lucky and funny, but on board the ship it's just always serious. Serious work that he is the captain.' "And that was the tumbler for me.
"I explained to Rich, I will say things you never said and we will be places you never were, but if we do this right thematically we will be spot-on with the nature of what happened to you and how.
"It's a very environmental movie, shooting it as we did on board more or less an identical ship to the Alabama at sea and in some very small confines. We were always searching for a combination of procedure and behaviour that were going to be not just reminiscent, but very reflective of what really happened. And that's tough when you're telling non-fiction entertainment."
* Paul Greengrass was speaking at the world premiere of Captain Phillips at the New York Film Festival.
Who: Paul Greengrass
What: Captain Phillips starring Tom Hanks
When: Opens at cinemas October 24
