It's a sad but true contradiction that having great sports lifts the overall perception of the school, at least schools like OSU, UNC, PSU, and yes, Duke and Stanford too. Duke is not merely a fine non -ivy school; it is DUKE!!! And that enhanced perception of Duke (and the others) as something better than it is, is oddly, strangely, but most definitely to do with the performance on courts and fields of athletes who normally would have no business being admitted to those schools (spare me the rare exceptions please... they are rare and exceptions), and must certainly are getting easier standards and special treatment the regular students aren't.
Yet by winning championships wearing the school name (and that's about where the involvement ends), people think the school is better, the school gets more and higher quality apps, more general donations (not just athletic donations), and, not to be underestimated, more weight to throw around in their states and communities.
And LOSING sports are seen to HURT these things... in Pitt's case not so much applications, which have improved, but certainly all other areas. All because of silly games. Weird.
Conversely, when scandals do manage to get through the PR and complicit media barriers to the public, it bizarrely doesn't have a NEGATIVE impact on the overall school. People read the confirmation that UNC athletes were given totally fake classes for years...and just shrug. "Everyone knows the sports have nothing to do with the real school." Yet WINNING makes them think more FAVORABLY of the overall school. Bizarre.
Never over-estimate the intelligence or underestimate the rationalization abilities of the human beings I suppose...unfortunately Pitt administrators do just that.