I can imagine that it might make a difference at universities that have historically had a large international student population. Looking at this US News list, some with over 20% include NYU, CMU, URochester, BU, Brandeis. (I don’t know much about The New School which is first on that list.)
Edited to add: Just noticed other tabs on the same list. Some examples of others listed with >20% international that are not considered “national universities”: DePauw, Mount Holyoke, RISD, CalArts.