Decisive moments - my personal opinion - The Killers?

***** Contains Spoilers *****

Major moments in this movie? To me there are 2 core moments:
1. When he decides to take over the identity. [Obvious]
2. When he asks casually, if he had eventually seen that person in London, reading, and obtains a confirmation.
To me, this is decisive. He, being a photographer, has seen items in the dead man's belongings, and remembers. He remembers for the first time in London, on the bench in the sunlight, and he remembers in Barcelona. But he's in no position to find out if he's right, and what is going on. At first, she denies, then only conceded. And with a big smile (usually she's no friend of those). And now everyone is in the clear about everyone else.
This is why surprisingly, she concedes to leave him towards the end (knowing what will happen), and this is why he says 'what the *beep* am I doing here with you'. Both know the game that is being played. He gets his last confirmation from that passport story.
At some moments it reminded me closely of The Killers, where the victim knows whats going to happen, though rests calmly in bed, waiting. And here, I also think he knew since that decisive moment no. 2 what would happen. I even think he played with the situation by doing all to make the outcome look like the gunrunner - his new identity - will have died twice. He knows, but he doesn't care. He has given himself up since long. He would not have taken the other identity otherwise.