If that is in doubt, then reference should be made to President Hinckley's October 1999 Priesthood Session address.

http://lds.org/ldsorg/v/index.jsp?locale=0&sourceId=ff1b6a4430c0c010VgnVCM1000004d82620a____&vgnextoid=2354fccf2b7db010VgnVCM1000004d82620aRCRD

He said that BYU's athletic programs "have brought honor to the Church" (and honor is brought to the Church mostly by being successful, because the world rarely honors unsuccessful athletic programs).

Assuming that President Hinckley was right in saying that successful BYU athletic programs benefit the Church, then it should be understandable why we're puzzled by the many active Latter-day Saints who want to remove or reduce the benefits provided to the Church by successful BYU athletic programs. There are no scenarios in which successful BYU athletic programs don't benefit the Church, except those in which BYU's own standards aren't upheld: (cheating, embarrassing Honor Code violations, budget deficits, fan arrogance, etc...).

It is true that many of us BYU fans (including players) become more arrogant when BYU's athletic programs are more successful, but the solution to that problem is to preach and practice humility (e.g. President Uchtdorf's October 2010 Priesthood Session address). We BYU fans, like all Latter-day Saints, could work to become less arrogant in all aspects of our lives in addition to sports, regardless of our reasons for being arrogant.

(Thanks again to shazbot, one of CB's Ute fans, who helped to refine my thoughts on this subject.)