Woops, I forgot about this thread.
Old school Traveller was very much part of the "story depth comes in the retelling" camp. The game relied heavily on random factors even outside of character creation. There were tables to randomly generate almost anything. The game, even more so than other old school games, could easily wind up being a series of mechanical challenges and puzzles for the player during the play session. The story depth would come in when the character's exploits were recounted. Traveller was a role playing game that was very much in touch with the "game" portion of that phrase.
I have observed this at work many times in my own groups. When we played Traveller: The New Era my players actually loved making up characters. In one group we never even played a session of the game. We made up characters several weeks in a row. By TNE the lifepath system was very in depth and complicated, the player would make many choices during character creation. They would roll through their life path and then come up with a story to make it all work. It became a kind of random story outline generator.
In classic Traveller many of our sessions looked like scout data reports and balance sheets at the end of the night. By the next week they had taken on a life of their own though. As we sat down for the next session the players had put all of the results from last week's game into context.
Another place I have encountered this behavior is with D&D henchmen. I would roll up random henchmen that would join the party. During the first session they were there the player saw them as nothing but a meat bag. They were hit points to be moved around. I would give them some minor personality, but let's face it, in AD&D the torch bearer probably wasn't going to be around long. As they made it through more and more sessions the players would bring them to life on their own, with very little input from me. I just responded to what they were doing.
Especially with overland adventures, it can be very hard for players to tell if they just had a planned encounter or a random encounter. There have been nights where, while exploring an uncharted land, my players only had random encounters. Next week when we sat down, there would be a story connecting them in some fashion. Of course I am going to take advantage of that.
I have even noticed myself doing this. In XCom the longer I had a guy in my squad, the more I put some kind of personality on him in my mind. There was absolutely no feedback from the game to support this. In fact I strongly believe that this is why that game remains so popular today.