1. pay enough attention to make sure you papers are in the right place then
2. flee without them, leaving them for the police?
Or leave a fake ID to send LE off on a snipe hunt.
I think most terrorists look at themselves as martyrs and think they're going to die and want recognition for it, especially since they are part of the selfie stick, me, me,me generation. I could see some of them leaving their ID in the vehicle for this reason, particularly if they are Americanized.
Maybe he didn’t plan it. Maybe he just snapped. Or, he just forgot his ID was there.