You might see elitism in her comment. I see an acknowledgment of her slim experience in this area. It is certainly true that she is a member of an elite having attended good schools and spent her life in the ambitious pursuit of her career.
There is a large class of people who spend their entire adult lives in the office or commuting to and from work. The closest they come to an outdoor sport is the time they spend on a golf course with the other people from the office. That sort of life may sound cartoonish to many people here.
I remember a few years ago, inviting a couple of judges to come to the range with me. Neither had ever shot a firearm. However, at the invitation. These girls rolled their eyes and flatly refused.
Apparently, Kagan did not do this. She either asked to come along or accepted an invitation. This indicates an openness that we might not expect from someone of her life experience. I concur that this holds out only a hope which may be slightly more than we had about her before.