Money as a factor in PhD admissions
Top-ranked schools generally commit to offering accepted candidates a certain level of support during their graduate candidacies. Therefore, finances must play a role in how many students they can afford to admit: if you only have sufficient financial resources to support 30 students, and 40 enroll, you're in for a bit of trouble. Thus, the students who are most desirable are those who can provide their own funding, in part or in whole, via external or internal fellowships or "matching funds" from the department. This frees up money that can be used on other students. (I would imagine that in math, much of this funding is awarded in the form of teaching assistantships rather than RA-type positions.)

This makes deciding how many students to admit a difficult challenge. Top students will have competing offers, and thus universities need to admit enough students to make sure they fulfill their research and teaching needs, but need to not be overly generous in making offers, in case yields exceed expectations.

As far as diversity goes, I agree with the assessments in the article you linked to: diversity only comes to play after candidates have cleared the qualification bar.