X, you always raise a good football centered question or make one in comment. I'll always appreciate your work on site.
As to topic, I tends towards an explanation that points to Bill Bellichick and his directions.
How is it, that his teams have always been fully functional with just a top notched quarterback on offense? Simply, a sharp throwing quarterback is able to throw all level and distances well. This leaves many more options on the board than simple putting out a stamped response as to team direction.
Maybe a quick comparison might focus my statement.
Bill bases his weekly scheme and mode of attack based upon beating the weaknesses that an upcoming opponent has on it's team. He doesn't throw extensively at a team that leads the league in pass defense...but in a selective manner that uses a tight end that just can't be stopped without a double team.
If a team is poor at run defense...the Patriots get a good dose of running the ball. That is how a lower round running back can produce 200 yards of rushing and get something like 4 touchdowns.
On defense, he has a complete shutdown cornerback, Revus, that he can adjust every element of his defense around to attack weak areas of an opposing offense. This means his defense can adjust and attack an opponent's offense as well.
The Cowboys, employ an understaffed bend but don't break defense...but while on offense, sends out the same scheme sequences week end and week out. But even this offense has weaknesses that are easily exploited.
The biggest eye sore for a Cowboy's offensive series, is cramming the box with a coordinated run blitz set, as the Cowboys still attempt to run at all odds to start off.
Double this, with an aggressive pass blitz package on passing downs, and those short passes and inside slants aren't being completed by Dallas.
To complete this thought, Dallas does not meet challenges to it's own weaknesses well...nor does it exploit an opponents effectively to gain advantage.
And defensively, Dallas at least needs to stop the run...as this will level general play between teams, a lot.