Street and Smith's 2005 College Football yearbook summed it up quite nicely: "Wake up the echoes. A two-year study convinced Notre Dame to begin playing seven home games instead of six, beginning in 2009. Now that a permanent 12-game season is a reality, Notre Dame is considering playing neutral-site games once a year in cities like New Orleans, Dallas, and Chicago, just like the Irish did back in the days of Knute Rockne. Notre Dame also plans to play Navy in Dublin, Ireland, for the second time since 1996."
The above appears consistent with other press releases and prime college sports publications. If Notre Dame plays three BE fb games, that would not be unusual for an independent. It would not be unusual even if Notre Dame was not a member of BE basketball.
What is clear is Notre Dame has affirmed its football independence, and has not publically announced any intention for joining any conference in the near future for football.
I really question Villanova will be pursing 1-A football, given their history, and their current lack of means to compete with the eight BE fb members. The eastern services academies, particularly Navy, are committed to fb independence. Army's recent ill adventure with C-USA should hold them at being fb independent for awhile.
Conference membership, among other important things (marketing, bowl agreements, championships, revenue sharing, etc.) is essentially scheduling. And scheduling, has to be equitable or near equitable in terms of the number of conference games each member plays. A bowl can enter into agreements with multiple conferences and/or independents. Such, does not mean mutual membership.