The history is this:
Pitt got passed over by the Big Ten in 1950 for Michigan State, and that was after spending most of the 1940s putting its program under the auspices of Big Ten and adopting Big Ten purity rules (while other Big Ten schools completely flaunted them) and playing a largely Big Ten schedule. This only is a decade removed from Pitt's most dominant period of athletics, in all sports, in the 1920s and 30s.
In 1981, Pitt was invited to the Big East primarily to foil Joe Paterno's plan to steal Syracuse and Boston College for his own conference. It was not invited because of its basketball tradition or its secular heritage. It was a pure strategic move to keep the fledgling conference intact. The invite would not have come in a vacuum.
In the late 1980s, Pitt again was not selected for the Big Ten despite behind-the-scenes campaigning to come in with Penn State as #12. And keep in mind that was before media markets mattered for TV networks like they do now so there wasn't the concern over market duplication or a need to open new tv markets. This snub followed what was Pitt's second most dominant athletic period and was just over a decade removed from a national title.
By the mid-1990s, Pitt was coming of decades of facilities and athletic program neglect and meddling that culminated with one of the nation's worst combinations of football and basketball which was accompanied by a booster apparatus that was weak and scandal ridden, an athletic department that was literally in shambles, and a university that was in its own financially precarious situation with an apathetic student body, disenchanted faculty (with significant segments calling for Pitt to drop out of major football), and highlighted by the fact it was literally having trouble filling its beds. When the ACC was formulating its plan to raid the Big East and establish itself as the Eastern conference in the late 1990s and early 2000s, Pitt was never seriously considered.
Therefore, there is absolutely no historical evidence that Pitt would have gotten invited anywhere based on its name or tradition, at least through 2003.
In fact, I think it is more than safe to conclude that if conditions were near the same in 2011 as to those circa 1996, Pitt may not have been invited into the ACC. The collective stink of the athletic department, terrible local/regional support, and the abysmal athletic facilities of the 1990s certainly would have been enough for Pitt to have lost its Power Conference status. My goodness, BC with almost no sports history, was still line ahead of Pitt in the early 2000s. Internal conference politics played a little bit into that, but such was the condition of Pitt.
Not to be lost on here is that a primary reason the Big East was able to retain power conference status in 2003, following the ACC raid, was Nordenberg essentially taking over leadership of the football schools and holding the Big East together. It required a tremendous amount of effort. Otherwise, Pitt's status as a major player (as well as perhaps even that of SU and WVU) may have ended right there.
Without the new and renovated facilities (which were extensive and across almost all sports), the demonstrated enhanced financial commitment over prior administrations, the behind the scenes work to retain power conference status in the early/mid-2000s, and the proactive behind-the-scenes moves of the prior administration to look for new conference opportunities circa 2010-2011, it is far from a certainty Pitt would be where it is today... and where it is today is a place where its athletic revenue are up 35% due solely to moving into the ACC. This is why the last two years, and only why, Pitt has been able to spend more on coaches and facilities.
People have a right to dislike Pederson or Nordenberg for their personalities or decisions tearing down Pitt Stadium or messing with history in switching logos or bumbling coaching hires, but sometimes people are in the right place at just the right time and serve those circumstances well. The problems of the past 15 years were largely institutional in scale, not on the scale of logos or individual hires. Now circumstances have changed, and it is the perfect time for new blood and we might have gotten some of those new blood hires right.