I get a better correlation looking at the Cowboys rushing attempts per game.
In 2012, the Cowboys lost all games when their rushing attempts per game were less than 90% of the season average.
They lost 1 game when their rushing attempts were between 90% and 100% of the season average. They had a -3 Interception Ratio in that game.
They lost 1 game when their rushing attempts were over 100% of the season average. The final score of that game was 31-29. The opponent had a Special Teams touchdown. Without the ST touchdown, the score would have been 24-29 in the Cowboys favor.