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Maybe the year that both Boise St and TCU finished undefeated (along with Cincinnati)? BSU used to schedule pretty tough, and had a several-year run of excellence rather than UCF which jumped up from bad results to undefeated really quickly.
But that doesn't necessarily jive, as they weren't passed over by 11-1 non-champs. There were only 2 slots in those days and there were two P5 undefeated teams ahead of them.
In all honesty, undefeated G5 teams are not all that common. Not to say they're truly rare, but for *any* team to finish undefeated is difficult. Which is why I think they should have a legitimate shot at finally proving they're worthy.

2016 Western Michigan 13-0   L Cotton Bowl vs #8 Wis
2010 TCU 12-0   W Rose Bowl vs #4 Wis
2009 Cincinnati 12-0   L Sugar Bowl vs #5 UF
2009 TCU 12-0   L Fiesta Bowl vs #6 Boise
2009 Boise State 13-0   W Fiesta Bowl vs #3 TCU
2008 Utah 12-0   W Sugar Bowl vs #4 ALA
2008 Boise State 12-0   L Poinsettia Bowl vs #11 TCU
2007 Hawai'i 12-0   L Sugar Bowl vs #4 UGA
2006 Boise State 12-0   W Fiesta Bowl vs #7 OU
2004 Utah 11-0   W Fiesta Bowl vs # 19 Pitt
2004 Boise State 11-0   L Liberty Bowl vs #7 UL
1999 Marshall 12-0   W Motor City Bowl vs Unranked BYU
1998 Tulane 11-0   W Liberty Bowl vs Unranked BYU

I don't disagree, I just get tired of the complaining from the G5 fans.  Those conference schedules are complete crap so don't complain when you play a crap OOC, a crap conference schedule and don't get into the CFP.  Sure, Ohio State and Bama have advantages that UCF couldn't dream of, but I'm not interested in making a level playing field, I'm interested in putting the best four teams in the country into the CFP.  

I don't think you're interested in getting the four best teams in. I think you're interested in getting the four most accomplished in. And that's fine. In the current context, it's a system that disqualifies half the teams at this level. And if we're honest about it, that's fine. What's weird is the anger from those in the privileged spot ("complete crap" crap, crap, crap). This is a sport that hates upstarts, a fact that never stops seeming a hint weird. 

UCF has a humongous advantage if we simply let in all Conference Champions or select solely based on record because their schedule is ridiculously easy compared to any P5 team.  They don't have the week-in, week-out grind of playing competent opponents.  Really?  What were UCF's best wins (pre-bowl because we are talking about at the time of selection)?  Memphis (twice, home and neutral)?  
Using Sagrin's rankings, Ohio State played (final ranking because I can't find pre-bowl):

• #4 Penn State, won at home
• #6 Oklahoma, lost at home
• #7 Wisconsin, won at a neutral site
• #18 Iowa, lost on the road
• #23 Michigan State, won at home
• #26 Michigan, won on the road

#32 Memphis was UCF's best pre-bowl opponent so Ohio State had six games against better teams than the best team UCF played all year.  
Here is the same list for Bama:

• #8 Auburn, lost on the road
• #17 MissSt, won on the road
• #19 LSU, won at home
• #28 Florida State, won at a neutral site

So Bama was 3-1 in four games against teams better than any team that UCF played and Ohio State was 4-2 in six games against such teams.  It is NOT CLOSE.  A G5 team needs to play a ridiculous OOC to get close to even but it also isn't impossible.  It was pointed out upthread that last year Houston beat P5 Champion Oklahoma and also played Louisville.  That is the kind of schedule that could make it.  If UCF had replaced Austin Peay and Maryland with quality OOC opponents then I think they would have had an argument.  

We come back to that "humongous" advantage. Assuming every UCF team is of top-10ish quality, then they would totally have an advantage. But they're not. UCF was winless three years ago. Did they have a massive advantage because the league was weaker? Do mid-major teams have an easier time getting into the basketball tournament? Nope. If UCF builds a top-10 team, it definitely has an advantage in going undefeated (but it's worlds harder to build that team). It has a disadvantage in that it needs everything to line up to have a shot. Again, it's an unbalanced sport. No need for the haves to complain about those advantages held by the have-nots 

What's interesting about the Oklahoma/Louisville thing is it shows how hard that is. If they catch those teams two years prior, it's 8-5 Oklahoma and 9-4 Louisville that didn't beat a team with a pulse. Houston didn't play for the Cardinals to get a Heisman winner (Oklahoma under Stoops was probably always a good bet, granted I bet Houston never thought it would have a team that could win)

If they have a playoff that lets conference champs of non-P5 conferences in, why wouldn't Arizona State move to the MWC and get into the playoffs every year?  Why wouldn't Illinois move to the MAC?  

The G5 or Other5 or whatever you want to call them are voluntarily participating in a system in which they cannot finish #1.  That's an odd choice, but it has been their choice.  Yes, they should move down.  And yet year after year, FCS teams keep jumping up instead, to join in with the ever-growing group of football teams that have no chance at #1.  Seems to me these ADs at Georgia State and App State and UTSA have some 'splainin' to do to the actual players themselves.

Seems odd.

That's the issue - but in the UCF vein, let's look at Utah.  The Utes have multiple undefeated seasons as a G5 school within a 5-year period and have nothing to show for it.  Okay, they say, we'll join a P5 conference, so that our next undefeated season yields a championship (what I'm saying UCF needs to do).  

Great.  What's Utah done since joining the big boys?  Jack squat.  Hmm, I wonder why?  Life's harder without a high school schedule.  UCF would realize that, too, but then the championships are earned.