Cords and sweaters are a natural pairing, since they're both pretty much cold weather clothing items. (Nobody muddy the issue by pointing out that there are corduroy shorts, or that he wears sweaters on 90 deg. days in August.)
A white shirt adds little color interest to the equation, but if you're already talking fern green and burnt orange, the last thing you need is to add some additional color to the mix. Besides, under a crew neck sweater, just how much of the shirt will even be visible? The sweater takes the shirt down to the level of a minor accent piece.