The difference the way I perceive the left right discrepancy may have a large cultural component. There was an old youtube clip of the Iraqi's doing exercise under US troop guidance. There is a certain degree of prejudice implied by the clip but they are of course as competent in using their bodies as any average American. The question then occurs to me why do they have such a "foreign" reaction to our calisthenics? My sense is they do not see what I see when I watch the exercise. I would not look as good as the troops but I would actively be searching them for the cultural structured cues to imitate. Like yesterday in the park it feels to be for me a very right side mode activity. I would quite likely look as silly to them doing activities that are Iraqi in origin. I doubt I be able to visually discern the differences that would mark me as a foreigner.
Cultural variation in eye movements during scene perception
Thus, it appears that differences in judgment and memory may have their origins in differences in what is actually attended as people view a scene.