There are a couple of comical non-sequiturs in the NCAA's response. Here's one (quoting only part of the Q&A):
Q. Some representatives from college athletic organizations have justified the tax-exempt status of college sports based on claims that high-visibility programs help sustain a large pool of student applicants and generous financial contributions. Neither of these arguments is valid from a Federal standpoint. Federal taxpayers have no interest in increasing applicant pools at one school opposed to another.
A. Many nonprofits engage in activities designed to increase membership, visitors and revenues. Symphony orchestras schedule “old warhorses” that attract more patrons, visibility and contributions than less-“accessible” works. Similarly, art museums schedule “blockbuster” shows of popular artists or artistic movements designed to draw crowds, raise visibility and, again, to encourage membership and contributions. Many charitable organizations advertise in one form or another – on television, on radio, in the print media and by direct mail.
The NCAA is avoiding the question. The question is, what interest does the federal taxpayer have in exempting income derived from activities whose primary purpose is to get more students to attend (and alumni to donate to) one university versus another. The NCAA characterizes the issue as one of a non-profits right to promote its activities. Symphonies are not usually directly competing with other symphonies. The NCAA members, by contrast, are directly competing. What Thomas is asking, and what the NCAA is not answering, is what interest does the federal government have in subsidizing this competition. If the mission of the NCAA member institutions is to promote education, should they really care whether a student chooses their university over another credible institution?