” Oddly enough,the SEC didn’t have quite so many national champions from the 1980s through the mid-1990s when the process of selecting national champions actually favored independent teams that weren’t locked into specific bowl games as conference champions. That’s why Penn State,Miami and Notre Dame won a disproportionate number of national titles in that brief stretch”
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For example, let's suppose Alabama finished a regular season as SEC champion and they were ranked #1 in the country. Let's also suppose that Penn State was ranked #2 and Nebraska #3. As SEC champion, Alabama would play in the Sugar Bowl. As Big Eight champion, Nebraska would play in the Orange Bowl. Penn State, as an independent team with no obligation to play in a bowl as a conference champion, would simply accept the invitation from the Sugar Bowl for the "open" spot against the SEC champion -- which meant they'd be playing for the national title against the #1 team.
Nebraska, meanwhile, would go into the Orange Bowl in the #3 spot knowing full well that they'd never win the national title even if they beat a strong opponent by 40 points.
If the #1 and #3 teams were reversed and Nebraska was #1 going into the Orange Bowl, then Penn State would accept the Orange Bowl bid instead of a Sugar Bowl bid and Alabama would be out of luck.
This is why you had those independents like Penn State, Miami and Notre Dame playing in so many bowl games that ended up deciding national titles back then. As independents they were always in a position where they could get the most favorable matchup instead of being automatically assigned to a bowl as a conference champion.
Notice how Penn State stopped playing in national title games once they joined the Big Ten. Big Ten and PAC-10 teams always had the most difficult time winning national titles back then because the Rose Bowl was the one major bowl where BOTH teams were determined by conference titles. So if Ohio State was ranked #2 and was the Big Ten champion, they'd NEVER have an opportunity to play against a #1 Alabama or Nebraska and might even be forced to play a team that wasn't in the Top 10 but happened to be good enough to win the PAC-10 championship.