One year Georgia beat Alabama for the SEC championship, Alabama beat Georgia for the National Championship.
In 2003 Oklahoma was crushed by Kansas State and lost the conference championship. Nonetheless, due to its "strength of schedule," Oklahoma was jumped over USC to play in the BCS championship game, even though USC had won its conference and had only one loss, which came after triple overtime.
Oklahoma deservedly lost the BCS championship game, while the Trojans beat Michigan in the Rose Bowl to win the championship according to the coaches' poll. To this day, USC claims to be the 2003 National Champion.