I’ve heard folks refer to Duke and Vanderbilt as “Southern Ivies,” but Auburn? Never. It’s a public uni for one thing and has always been best known for its engineering strength, something Harvard didn’t even have until recently.
Every private school aspires to be Harvard because, like it or not, they are the most difficult (or among a handful of most difficult) to gain admission to, and they have a HUGE endowment. Public unis have a different mission. I think most public flagships aspire to be in the same cohort as Berkeley, Michigan, UCLA, Virginia, and UNC. Those are the premier public schools in the nation (along with some non-flagships like Georgia Tech), and probably a few others I’m overlooking. (I personally think of Texas that way.)
Is US News only polling Alabama guidance counselors when it’s rating Alabama and Auburn? That would be odd, wouldn’t it?