Not a single one of those quotes has anything to do with 'balance' or rushing the ball.
Two are about fumbles and two are about 3rd and longs.
Just adding "and balance prevents this" doesn't make the quotes germaine. Basic logic. You could just as easily say "and eating candycanes at halftime prevents this" to those quotes, and it would logically follow in the exact same way.
Incidentally, the 2012 Patriots turned the ball over MORE than the 2011 Patriots. Not that it has any bearing on the discussion, or that it was a large gap. SO I'm not sure the whole "running it 3 times more per game = less turnovers works". In fact, the season (albeit by a slim margin) proves that. But they are essentially identical numbers anyhow, like every other efficiency number, that proves the 2-3 more runs per game resulted in no real impactful increase in efficiency.
Not to mention, they were actually a worse TEAM this season, taking one more loss despite having a statistically superior defense and a statistically identical offense.
Again, per the SB to Prolate:
Scoring TDs on 25% of your drives is very good, both the Pats and Giants did this. The top offense in 2011 scored TDs on 33% of their drives, the bottom scored 8.4% of their drives. A team scoring TDs on 25% of their drives in 2012 would have been ranked 7th in the league.
Scoring 2.3 or 2.5 ppd, which they both did, would have placed both in the top ten again. The best team in the NFL averaging 2.8 ppd and the worst averaging 1.07 ppd.
However, allowing those scoring efficiencies would have placed both defenses squarely in the bottom five.
Neither defense was very good in the Superbowl, the Giants made one more play than NE, the forced safety. The INT was basically a punt, because it ended with the Giants on their own 8 yard line. Not a good play by any measure, but not a tragic play in the grand scheme.
The problem is that NE's defense did nothing. Nothing at all really. Every drive the Giants had resulted in at least THREE first downs, a FG, or a TD. That is abyssmal. Give the Giants some credit for being incredibly efficient, but knock the Patriots defense for putting up one of the most abyssmal Superbowl performances in recent history. Literally, there has not been a less efficient defensive performance than that in decades. Even the Raiders who allowed 34 points to the Buccaneers intercepted them once and forced two three and outs.