Rules question: Placement of ball on change of possession

on downs.

This question is based on the Saints' 4th down attempt that left the ball inches short of the Chicago goal line.

Let's say that the offense runs a play on fourth down, but fails to secure a first down. And let's say that the play left the leading tip of the football exactly at the defense's 10 yard line.

My understanding was that before the defense takes possession of the ball, the refs must move the ball the length of the football so that the leading tip of the ball is still exactly on the 10 yard line, but since the ball is now going in the opposite direction, the rest of the ball is now resting across the 10 towards the 9 yard line.

The purpose of the move is not to give a football length of advantage just because of the change of possession.

In the Saints-Bears game, the Saints appeared to be about 4 inches short of the Bears' goal line when the Bears took over on downs. Following the above rule would require the ball to be moved so that the leading point of the football (for the Bears) is still 4 inches from their goal line, but that would leave most of the football inside the end zone when the Bears take over on first and 10.

Clearly that is an unreasonable result, so there must be an exception to the rules for goal line situations. Anyone know this exception?