The moviemaker asked Damon to appear in the biopic, about Latino revolutionary Che Guevara, and he was quick to sign up to the picture.
But the shoot clashed with overseas promo work for Damon's 2007 action thriller - so the actor used the opportunity to get free flights from the U.S. to Europe for him and his wife Lucy.
He tells Britain's Total Film magazine, "Steven called me and says, 'Will you do a day on Che?' They were in the south of Spain. I said, 'Lucy and I are going to be there.'
"I had some press to do there for The Bourne Ultimatum. So the studio flew us there and we snuck in because Che was the lower-budget movie. We let Bourne get us to Europe and then I went down (to film Che)."