This is not an argument that applies much to, say, the mighty Carnegie Mellon Tartans.

Even at schools with actual athletics programs and budgets, most PhD students are paid with grant money won by their advisors, or through government fellowships. Not by the university. (I'm a PhD student at CMU paid with NSF grant money.)

Also of note, CMU just introduced a new presidential fellowship to fund undergraduate and graduate students in all fields [1].

1: http://www.cmu.edu/news/stories/archives/2015/september/pres...