Moving Game to Dec 3rd

There has been a lot of talk about not being able to move the game to Dec 3rd because of having to then move the SEC Championship game to Dec 10th which would mean delaying the selection of the 4 playoff teams and bowl game selections. My question is what about the Army Navy game which is scheduled Dec 10th. I know the likelyhood of this ever happening is slim to none but what if one year one of those teams were in contention for one of the 4 spots. What would they do then ? Maybe I am missing something but aren't they eligible ?