Other than WVU and Pitt, are there any Big East teams who would compete for a national title, even undefeated?

Cincy was in a BCS game last year, and started unranked this year. Went undefeated, and never sniffed the championship game. It doesn't matter what sort of decent runs Cincy, or South Florida, or Louisville, or Rutgers have, they won't compete for a national title, because some schools are considered college football schools, and others aren't.