Michigan's 1997 national championship team played all power conference opponents (Baylor, Colorado, Notre Dame).
In fact, from the 40s until the mid 90s, Michigan almost exclusively played power-conference programs in non-con play, with the exceptions being service academies and the Ivy League when it was still relevant. That was partly because they could get guarantee games from some of those programs (even schools like Florida State, Miami (FL), Georgia, Arizona, Virginia, and Maryland)..... Obviously that's no longer possible, though.