The piece of the puzzle you guys are missing is:
When you are aggressive and go for takeaways, if you miss the takeaway, it often results in a big play in yards and/or a TD.
The second problem is you get the takeaway. But your offense sucks and goes three and out.
You are right back on defense.
Smart teams are more willing to be aggressive when they are in front when they have momentum.
Going for the turnover when you're behind might seem like a good idea, but if you miss.....you dug a deeper hole.
Now, you're down by ten inside 2:00 to play, the offense have the ball on your side of the 50, do you play aggressive even if means you lose by 13 or 17, or play tight to prevent another score?
Its hard to evaluate every single play that produced the stats on that page.
The 2009 Broncos have been mentioned. The Denver defense finished 12 overall, 3rd in passing, and 26 in rushing. The offense was 20th overall, 13 in passing and 18th in rushing.
So the first 6 games Denver held opponents to 66 points while scoring 133. Their next four games the offense scored 37 while defense gave up 117.
It appears from those stats when the offense was scoring points, the defense was able to do its job. But when the offense went dry, the defense started having problems.