Not sure if this is the type of thing you're looking for, but just in case....
The 1908 LSU Tigers team posted a perfect 10-0, outscoring opponents 442-11 on the season. Near as most accounts can recover (and it's not easy to find articles within the time-frame, as opposed to historical pieces after the fact), LSU would've been selected by most of the various polling organizations of the time as a national champion, although it appears that wasn't nearly as much of a thing as conference champions at that time. However, Auburn sportswriter Grantland Rice accused LSU of paying QB Doc Fenton and some other players and then convinced Tulane to join in the accusations, and due to the shroud of controversy the SIAA sportswriters picked Auburn as the 1908 SIAA (forerunner to the SEC) champion and left off all LSU players from all-conference selections.
The SIAA conducted an investigation, eventually clearing LSU of any wrongdoing, but the votes were already cast prior to the investigation's conclusion. The various governing bodies, including the NCAA, retroactively recognize LSU as national champions, although the school itself does not claim 1908. I wish they would.
So I don't know how "screwed" you can say a team is that was later recognized by external governing entities as a national champion, but their season at the time was certainly for naught. If nothing else, it proves that Auburn has always been Auburn, since the dawn of time.