Gilroy, who has written all four Bourne instalments and makes his franchise directorial debut on The Bourne Legacy, spoke with Vulture about the somewhat chaotic journey the series has had.
"It's been somewhat well documented that [the Bourne franchise] not been well organised; it's not been the space programme," Gilroy mused. "It's been a very shambolic success.
"Still, there's something about the DNA that got started in the beginning... there's been an integrity to it, and I think having Matt Damon pin that integrity down and having Doug Liman's funky, dirty-on-the-ground filmmaking and Paul [Greengrass's] journalistic integrity, that's helped.
"As bent and crazy as the process got, and as many people didn't get along, no-one ever tarnished that basic element of truth, and that's been the one thing that's held it together."
Damon played the eponymous lead Jason Bourne in the first three films, and is replaced in The Bourne Legacy by Jeremy Renner as new agent Aaron Cross.
Several reports of a potential sequel starring both Damon and Renner have emerged over the past few months, with Renner saying that he would love to work with Damon and Damon stating that he expects to return to the franchise.
Gilroy has recently said that he considers Renner "perfect casting" in the role.
The Bourne Legacy will be released on August 10 in the US and August 13 in the UK. Watch a clip below: