Your quote "People outside of ND may disagree with this line of thought but people outside of ND do not count regarding this decision" is absolutely true.

As for being America's "Catholic University", you are right on a "perception" level since most people know about Notre Dame football, Touchdown Jesus, and the fighting leprechaun. As for its traditional Catholicism, it isn't as Catholic as The Franciscan University of Steubenville or The University of Dallas. Notre Dame, like most American Catholic universities has become very secularized over the past 40-50 years. Today, there's not much difference between most Catholic universities and public universities. Georgetown and Marquette are almost ashamed of traditional Roman Catholicism. As a Catholic, I only see Notre Dame as America's Top Catholic college football program. They have some work to do to win me over as "America's Catholic University'".