Regardless of the issue of conference affiliation, it can be stated for the record that the current "non-BCS" schools have more guarantees in the way of playing in a BCS-level bowl, which obviously is not saying a whole hell of a lot. Florida State is one school that undoubtedly propelled itself from "non-BCS" status to BCS-level status as an Independent, and without much argument it can be asserted that the ACC began to operate at the level of Big Ten, Pac-10, SEC, etc., by virtue of Florida State's membership. I don't necessarily know that the same can be said of Miami in regards to the (current) BIG EAST (save me the drama Clemson fans). Alas, FSU is defintely a rare exception (as is Miami), and its rise took place during a period when non-Notre Dame Independents were not persona non grata.
Nevertheless, it must be conceded that Louisville, BYU, Tulane, etal can make more of a tangible argument that they now are able to compete at the "highest level" than before, which as I said earlier, is not saying a whole hell of lot, considering notoriously overlapping and contradictory BCS rules, most notably the "Top Six," "Notre Dame," and "3/4" provisions in place under the BCS framework.
It will again be stated that Louisville's appearance in the Fiesta Bowl took place under the irreplaceable set of circumstances and that, after foregoing an automatic bid to the Holiday Bowl for its champion in 1985 (the year following BYU's undefeated season), the WAC returned to the Holiday Bowl in 1986 after it realized that no one (at least not at the then-Big Five bowls) was going to be recognizing a national power status for Air Force or BYU anytime soon. For the record, Air Force finished with one loss that year (1985), and wound up going to the moribund Bluebonnet Bowl as opposed to say the Cotton or the Fiesta (the Cotton Bowl took an 8-3 Auburn team by virtue of the fact that if featured Heisman Trophy winner Bo Jackson).
The only real record that I can think of where "non-BCS" teams advanced to "BCS-level" bowls (post-1960s/early 70s) are three instances involving ACC teams, prior to the addition of Florida State, namely Clemson (1981, Orange Bowl, undefeated season), Maryland (1976, Cotton Bowl, undefeated regular season) and Virginia (1990, Sugar Bowl, 8-1 record at time invitation was accepted, lost final two games; 1990 was a bizarre season on many levels in college football perhaps epitomized by the fact that the recognized AP champion, Colorado, finished 11-1-1, and featured an infamous "victory" at Missouri; also note that UVA didn't wind up becoming ACC champion that year, UPI champ Georgia Tech did--however, at the time the Sugar Bowl issued its invitation, the ACC Championship was still up for grabs, with GT holding the tie-breaker over UVA but only leading by a half-game(?) in ACC standings: GT had defeated UVA, but tied UNC). While those teams (Clemson, Maryland, Virginia) are all BCS teams now, it is arguable that they were not "BCS-level" at the time of their bowl appearances, but then again, the lines were not drawn as distinctly then as they are now in that regard. This was an era where nothing was guaranteed for the ACC, case in point that in 1979, the ACC champion (NC State) did not go to a bowl, the 1980 champion (one-loss North Carolina) went to the Bluebonnet Bowl, and the 1981 champion (Clemson) went to the Orange Bowl (could this have happened if Clemson had not defeated consensus #2 Georgia??) and undoubtedly this was predicated on its status as being the only undefeated at the end of the regular season...if say, Penn State and Alabama were also undefeated, Clemson would have been SOL (also see BYU, 1984). d**n that post was long, but I hope it is informative and provides context.