You've got to remember that the absolute cardinal imperative of the CFP committee is perpetuating the legitimacy of the CFP structure and process. Forget Illinois and Ohio State, the committee is not going to step on the toes of the Big Ten Championship Game as an entity and TV property like that.
They took OSU in 2014 to avoid the impossible choice between Baylor and TCU.
They tried to delegitimize Cincinnati until the bitter end in the week-to-week polls (as they do with all non-P5 contenders) until it reached an inflection point where leaving them out would undermine the public perception of the process and then it flipped.
They are very conscious of the job they're doing.
I do think Lysol does make a valid point along with your own. Truth is this would be a fairly bizarre occurrence as the precedent we would be looking at is one where 2 teams in a conference finish with the same 1 loss record after the championship game and there are 3 other more deserving teams ahead of them leaving one last playoff spot available. There is one very near instance of this (2008-09) in the CFP or BCS era along with a few similar ones:
2014-15: TCU (11-1) and Baylor (11-1). In this year, neither team was selected to make the playoff and there was no B12 championship game, but TCU's lone loss came @Baylor whereas Baylor lost on the road to a much weaker opponent. TCU also played the much stronger schedule. However in the final CFP rankings, Baylor was the 5th ranked team and TCU the 6th. In this case, Baylor would be our best comparable however it is important to note that Baylor had better brand recognition at this point than TCU.
2011-12: Alabama (11-1) and Oklahoma State (11-1). While these teams are in different conferences, in this year Alabama was selected to the BCS Championship while Oklahoma State was left out. Alabama lost their 1 game vs undefeated LSU and had the much better loss than Oklahoma State and a slightly better SOS, however Oklahoma State won their Conference and at the time was thought by many to be the more deserving selection for this reason. In this case, Oklahoma State would be our best comparable, and it is important to note Alabama had much better brand recognition than Oklahoma State.
2010-11: OSU (11-1) and Wisconsin (11-1). In this year, neither team was selected to make the BCS Championship but OSU's lone loss came @Wisconsin whereas Wisconsin lost on the road to a slightly weaker opponent. OSU played a slightly stronger schedule. However in the final BCS rankings, Wisconsin was the 5th ranked team and OSU the 6th. In this case, Wisconsin would be our best comparable and it is important to note that OSU had better brand recognition at this point than Wisconsin.
2008-09: Oklahoma (12-1) and Texas (11-1). In this year, Oklahoma was selected to make the BCS Championship, but OU's lone loss came vTexas whereas texas lost on the road to a similarly strong opponent. OU played a slightly stronger schedule. However, OU was selected B12 champion through numerous odd tiebreakers and in the final BCS rankings, Oklahoma was the 2nd ranked team and Texas the 3rd. In this case, Texas would be our best comparable and it is important to note that Texas had a much much better loss than us but were also not named B12 Champion.
2000-01: Washington (10-1) and Oregon State (10-1). In this year, neither team was selected to make the BCS Championship, but Oregon State's lone loss came @Washington whereas Washington lost on the road to a similarly strong opponent. Oregon St played a slightly stronger schedule. However, Washington was the 4th ranked team and Oregon State the 6th. In this case, Washington would be our best comparable however it is important to note that Washington had a much much much better loss than us and they had better name recognition than Oregon State at this point.
Ok, so based on the 5 similar historical cases, it would appear that in the 3 of them, the team most resembling Illinois was selected in the playoff whereas in the other 2 the team most resembling OSU was selected, so overall I don't think this is actually all that cut and dry. I agree with you it is more likely Illinois would be given a playoff spot than OSU in a scenario where both teams finish 12-1, but based on the historical data, I would have to agree with Lysol that this isn't necessarily a given