Wintermute had built Armitage up from scratch, with Corto's memories of Screaming Fist as the foundation. But Armitage's "memories" wouldn't have been Corto's after a certain point. (17.12)
The passage suggests that what separates people is not DNA but rather memories. Armitage and Corto have the same DNA, but different memories, so they're different people. Which makes sense. After all, identical twins aren't the exact same person when we're not speaking genetically.