Actually, this is inaccurate information. If you read the linked page a little more carefully, you’ll see that this is a special concentration in jazz studies, not a major, and it is designed to be combined with a major either in music or in a non-music field. As it says on the page linked, “The special concentration in jazz studies is designed for music majors as well as for those majoring in other fields.” @piranhavator, I don’t think the major you list will have much or any impact on your chances of admission, but you should not list jazz studies as your first choice major, as it will indicate that you have not done your homework.
As for the jazz program at Columbia, it is terrific, but you should recognize that it’s not the same as a conservatory/music school experience. That said, in addition to the jazz resources at the school, there is a wide range of jazz resources outside the school. Including a joint program with Juilliard if you’re lucky enough to get in to that (though it’s a long-shot so you certainly can’t count on it). My son graduated from Columbia and is now pursuing music full time. If you check my posting history, you’ll find a number of posts in which I discuss the Columbia jazz program, as well as the challenges of pursuing music at a conservatory level within the context of an academic college.