I would argue it is clearly and emphatically the former. A brand isn't a list of talking points, it's something that has emotional resonance with people.
In my heart I agree with you, but I'll advance a contrary opinion that I think will determine the way things will go. BIG is not about combines, corn and fall days, rather it is the confluence of academically oriented University Presidents and marketers. The BIG has the most comprehensive academic alliance to match the athletic alliance. If you don't think that is important look at what the ACC and SEC are trying to do in that regard and remember that imitation is sincere flattery. Academics will always be a significant hurdle for expansion.
But this isn't just elitism, it also is part of the branding. BIG schools are the combination of biggest and best schools in the country, with great graduate research and professional schools. This means that that BIG schools have a lot of alumni, that are making a lot of money. There is a reason why golf and tennis are on TV, and its not just ratings, its the "right" ratings for advertisers.
True unaffiliated sports fans might prefer the SEC these days, but advertisers will pay a premium to reach BIG alum. I think that is the brand the Delany is trying to expand.