It seems to me that one of the appeals of attending a nationally recognized college would be to interact with other students from across the nation. And from a more cynical perspective, it allows that school to be “nationally” recognized.
Out of curiosity, I downloaded the “residence and migration of first-time freshman” from the Integrated Post-Secondary Education Data System (IPEDS) database for a select number of colleges. I picked the colleges based on general prominence and an eye to geographic diversity–no sort of scientific rational involved.