The Seattle reference was tongue-in-cheek.
Example. Two offenses play the same defense.
Offense A
100 yards rushing
300 yards passing
65% completion ratio
35 passing attempts
20 rushing attempts
Win 24-21
Defense plays 7 men in the box.
Offense B
100 yards rushing
300 yards passing
65% completion ratio
35 passing attempts
20 rushing attempts
Win 24-21
Defense plays 8 men in the box.
The stats are going to look exactly the same, but the running game was more important to Offense B than to Offense A.
The correlation on passing efficiency would be exactly the same for both offenses.
The correlation on rushing efficiency would be exactly the same for both offenses.
Passing and Rushing are dependent variables and the simple statistics that are available don't define the exact dependence. The 8 men in the box vs 7 men in the box stat does not exist. Obviously, it is more complicated that just 7 vs 8 men in the box, but I'm just using that as an example; however, that stat would be much more informative that just rushing yardage.
It is the threat of the rush that caused the defense in the example to play 8 men in the box. If that offense gained the same yardage as the offense that played against 7 in the box, then it obviously is a better rushing offense, but the stats do not show it. The stronger rushing team probably also caused the defensive line to play run 1st more often which would limit their pass rush. There are several ways that a stronger rushing attack can help passing, but that won't show up in the simple stats.
If passing effectively was the only determining factor in winning and there was no dependence between passing and rushing, then LBs would cease to exist. All players would either be CBs or pass rushers.