Or not having a conference championship game actually gave them a shot if things fell the right way.
Lets see that conference championship scenario from a perspective where it doesn't help them.
Big 12 South (Tech, Texas, Baylor, TCU, OU) vs. Big 12 North (KS, Kansas, ISU, OSU, West Virginia): Baylor vs. Kansas State.
Either Baylor loses, and now having a championship game cost the Big 12 a spot, or Baylor wins but the committee is more impressed with Ohio State so they still get left out. Having a CCG is NOT the reason they were left out, and it can hurt just as much as it can help. Back when they had a Big 12 championship there were several upsets over the years that would not doubt screw teams over in the current environment.
Not having a CCG might hurt Notre Dame once in a blue moon, but it might also hurt their chances, and they don't need to have one with their strong strength of schedule as it is. Look at Alabama and Clemson - I'm sure given the option they would skip their CCG because it is only going to hurt their chances.
I'm not opposed to conferences having CCG - and I think that they can obviously help teams make that final statement (like Ohio State last year). But they aren't guaranteed to and it is only a matter of time before it screws over one of the conferences.