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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.  

Speaking of h2h, there are also famous controversies when the 2 teams tied.

In 1966, Notre Dame and Michigan State tied, but Notre Dame was voted nation Champion over MSU.

not only that, but bama was preseason #1 that year, went undefeated and won bowl game. only time in cfb history a team has been preseason #1, gone undefeated, won bowl, and not won the title.

i've seen some argue nd and/or msu played tougher schedules, and perhaps that's true. but it isn't materially different. bama played 3 teams ranked at end of season in coaches poll (only ranked 20 at this time), and 1 in ap (only 10 ranked at this time). all away from home (2 away, 1 bowl). bama went 3-0. nd played 3 in coaches and 2 in ap, 1 home, 2 away (1 h, 1a for ap), went 2-0-1 (1-0-1 ap). msu played 2 in coaches and ap, both at home, went 1-0-1.

bama was also back to back defending national champs (ap). though, similar to these arguments, it can be argued that bama shouldn't have won in '64 (lost bowl).

The operative term I think is "voted", like picking your homecoming queen or something.

The other one is "mythical" ...

I thought that happened in the 80's.

1972

osu playe din 4 straight, from 73-76.

in 1975 the b1g allowed more than 1 team to go bowling.

Facts don't care about my feelings.  

I seriously don't understand, especially after reading this thread, why so many are opposed to playoff expansion.  All of these teams seems like they were just randomly screwed out of something akin to a beauty pagent process.  Everybody votes their favorite.  

I really had no idea of all these old time controversies, only the ones from the last 25 or so years.  

The rule about back to back Rose Bowls had already been changed before the season started.

True, but that would have been a better tiebreaker than what they came up with.  The conference vote was all about alliances and had nothing to do with their on-field performance.  They should have just defaulted to their old philosophy of giving it to the team that had gone the longest without going to the Rose Bowl. 

This must have become the official 3rd tiebreaker rule again at some point.  Because Iowa went to the 1982 Rose Bowl following the 1981 season after they tied OSU with a 6-2 conference record.  First tiebreaker was h2h but Iowa and OSU did not play.  2nd was overall record but both were 8-3 overall.  3rd tiebreaker was which team had gone the longest without a Rose Bowl,  which was Iowa.