Back then the conference tie-ins were even more important than they are today.

You had Florida State and Arizona State both undefeated going into the bowl season. You had the Rose Bowl only willing to match up Big 10-Pac 10 (they were not part of the Bowl Alliance). So BYU can't play Az State (although they lost to tOSU anyway). And you had lots of very respected teams from Bowl Alliance conferences with one loss.

So the only way it happens is if the Bowl Alliance lets you play in their national championship game against (and beat) undefeated Florida State. I just doubt you get to play in that game, no matter what. As it was you got passed over by a number of lower ranked teams with the same record and didn't play in a Bowl Alliance game at all that year.