Princeton, CUNY, NYU, UPenn, and Columbia are all top-notch ethno/musicology programs in a highly desirable location, which means that they get about 100-150 applicants for approximately 2-3 spots every year. Therefore, admittance isn't just about meeting the requirements and being a good music scholar; it means also being a perfect match/fit for the department's research strengths, and then some extra luck on top of that as well.
Also, since music departments in academia tend to be small, being an easy person to work with is also an important factor, considering that these will be intimate colleagues for 6-8 years. Therefore, I assume the committee are looking for applicants with a least some humility. There is healthy confidence, but then there is flat out sanctimony. A desire of belittling all those who DID get in and who ARE successful will close the door on an applicant fast...