I believe Spielberg's intent is clear. Always fun to imagine a different interpretation, though.
Found a really neat article about that scene I suspect you'd both like.
http://coachfinstock.blogspot.com/2012/05/classic-scenes-jaws.html?m=1"Brody's isolation is symbolized when the scar scene begins, as he standing away from the table where the other two are sitting. Like the audience, he is a third party observer as the scene unfolds. His unwillingness to participate is further emphasized when he lifts his shirt to reveal what is obviously an appendicitis scar. He believes his injury is not significant enough to share with the others, so he lowers his shirt and returns to his role as the observer. Quint and Hooper laugh as they compare scars received from various adventures. The conversation takes a dark turn when Brody questions a scar on Quint's arm. Quint admits he received it from his days in the war."
