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With all due respect to #3 USC, the teams most deserving of invitations to the Sugar Bowl are #1 Oklahoma and #2 LSU.
All 3 teams have 1 loss, and USC simply has not beaten anywhere near the caliber of teams that Oklahoma and LSU have beaten: Oklahoma has beaten #5 Texas, and LSU has beaten #12 Georgia twice.
Based on teams' current rankings, Oklahoma and LSU have each played 2 games vs. better teams than USC's toughest opponent, and they have each played 5 games vs. better teams than USC's 2nd-toughest opponent.
USC has not played a current top-15 team, and the Trojans are only 2-1 vs. the current top-40, despite playing #38 and #40
The best team USC has beaten is #18 Washington St., while The 2nd-best team USC has played is #38 Cal, which beat the Trojans.
Oklahoma and LSU have each lost only to a current top-25 team (#16 Kansas St. and #24 Florida, respectively), and they have combined for 9 wins over teams currently ranked higher than Cal.
As the following list shows, USC has posted only 2 of the 10 best wins by these 3 teams (based on teams' current rankings):
1. Oklahoma over #5 Texas,
2. (tie) LSU over #12 Georgia (regular season),
2. (tie) LSU over #12 Georgia (SEC championship game),
4. USC over #18 Washington St.,
5. Oklahoma over #19 Oklahoma St.,
6. LSU over #20 Arkansas,
7. LSU over #23 Mississippi,
8. Oklahoma over #31 Texas Tech,
9. Oklahoma over #32 Missouri, 1
0. (tie) USC over #40 Auburn,
10. (tie) LSU over #40 Auburn
In sum, the Trojans' top wins are over much worse teams than the Sooners and Tigers have beaten, and the Trojans' loss is to a much worse team too: Oklahoma and LSU deserve to play in the Sugar Bowl.