Meh. The whole "you can't rely on turnovers" argument is decidedly weak. NE was also a pretty good red zone team as well in the regular season, particularly in 2011, didn't help much. Everything is reliable, until it ain't. Even the great SF defense allowed 21 first half points to the same offense that NE held to 7 before collapsing in the second half.
As for the question at hand, you need to take a step back. You are analyzing this as if NE has had a gradual decline in defense over the last 4-5 years and trying to find a cause in there. The real source, however, is NE's failed defensive rebuild from 2006-2009 (really, you can go back to 2004 if you want to). Over those seasons, the Pats brought in a ton of bodies, not a one of them working out. This has led to an absence of heading-into-their-prime experienced starters. Holdovers from the old regime held on as well and as long as they could, but obviously that only lasts so long, hence the "gradual" decline.
Now, we are seeing the opposite end of the spectrum, a developing defense still getting their feet wet and learning how to play with each other. In 2012, for example, the defensive elder statesmen were Wilfork, Mayo and McCourty. Think about that for a second and how much it contrasts with 2003, when Mayo would the babe of the LB bunch by at least 2 seasons. And McCourty was even learning a new position last year to boot!
When you watch a football team, you are seeing the sum of their decisions over the last 5-6 years. That's been a drag on the last couple seasons, but it looks like a good thing for the next few.