There is certainly a diversity quota. If only the best is admitted without care for nationality, we might end up with an all international student cohort.
Admissions data at Princeton: http://www.princeton.edu/gradschool/abo ... ea/MAT.pdf
Looks like the number of internationals is around half of the total admitted. Which could mean that international students have a harder time as they have to compete with the rest of the world for 50% of the places, while USA citizens compete with locals for the other 50%.