The issue with Notre Dame isn't "are they the best fit?" ... but rather "who is a better fit?"
Let's assume that every school from the Big XII, ACC, Big East, and Vanderbilt is in play, and that the rest of the SEC, the entire Pac-12, and non-BCS schools are not in play.
Which of the schools in play has a better football program, going forward, than Notre Dame?
Texas, Oklahoma, Virginia Tech, Florida State, Miami, maybe Georgia Tech.
Which of the schools in play has a better academic reputation than Notre Dame?
Texas, Duke, Vanderbilt, maybe Virginia.
Which of the schools in play has better tradition than Notre Dame?
None, but Texas and Oklahoma are close.
Which of the schools in play has a bigger national audience than Notre Dame?
None, but Texas has a huge footprint in the southwest.
Yeah, Notre Dame, being a small, Catholic, non-AAU school isn't exactly a perfect fit for the Big Ten or the CIC, but who's any better? Texas, probably, but they've suddenly become the kid who pisses in the sandbox when he doesn't get the biggest pail. Oklahoma is a mega-power in football with huge academic and character issues. Georgia Tech and Rutgers and Virginia and whatever might be nice additions, but remember we are looking for four schools now, and would anyone seriously contend that Notre Dame isn't one of the top four candidates?
The Big Ten is in a good position right now with twelve solid programs and room to expand east, west, and/or south. The Big XII and the Big East will collapse eventually, if not this year then sooner rather than later ... the Pac 12 has been rejected by the Bevo-ites and is probably stuck looking at western schools like Boise State ... and the SEC isn't going to make a serious run at any Big Ten prospects. So we wait it out until Texas and/or Notre Dame realize that the Big Ten is their best home and then we take them and fill in the blanks, or we expand to superconference status on our time table by finding the best four from the dozen or so viable candidates that remain. Either way, we don't say "no" to Notre Dame unless they say "no" to us first.