Its not about time of possession. Its about tempo and pace of consecutive plays. When teams run a fast pace, no-huddle offense (see Auburn, Oregon, etc.) the defense can't substitute. Many of these offenses look to stretch the field horizontally with a lot of WR screens. So, you've got 300 pound defensive tackles and 260 pound defensive ends who are trying to rush the passer and then trying to pursue to the outside on all the horizontal offense. These guys get worn out after 7 or 8 plays of running all over the field. With no opportunity to substitute, the offense then runs the ball right up the gut passed a gassed defensive line. That's essentially the strategy.
Yes, letting your defense rest between series is helpful. But 300 pound guys aren't accustomed to running 20 or 30 yards per play for 8 straight plays. If that starts to happen, it really doesn't matter how much rest they got before the series started. All that said, I still think the point stands. A ball control offense can help keep the defense RELATIVELY rested and can keep a potent offense holding their helmets on the sideline. Shortening the game and limiting possessions can keep a lower scoring offense within striking distance.