The recongized national championship in college football since the inception of the BCS is the BCS not the AP. The AP is just a component - they can have their own national championship just like Saggarin if they want to, but it's not the real one.
If LSU had won the AP and USC had won the BCS, no one outside of Lousiana would be claiming that LSU was national champions that year.
Go whine on another thread. The AP National Championship trophies in Heritage Hall look like all the other AP trophies USC has won.
Note that unlike with USC, no one ever congratulates LSU on classiness.