The facts say I'm correct. Let's look at the facts from around the league in 2015 --
Teams that passed better went 202-54, a winning percentage of .789.
Teams that rushed better went 134-122, a winning percentage of .523.
Teams that passed better AND rushed better went 107-27, a winning percentage of .799.
Teams that passed better and rushed WORSE went 95-27, a winning percentage of .779.
Teams that rushed better and passed WORSE went 27-95, a winning percentage of .221.
Teams that rushed worse AND passed worse went 27-107, a winning percentage of .201.
So, teams that passed better than their opponent won almost 80 percent of the time, and it made almost no difference whether they also ran better (.799) or ran worse (.779) than their opponent.
Teams that passed worse than their opponent won only about 20 percent of the time, and it made almost no difference whether they ran the ball better (.221) or ran the ball worse (.201) than their opponent.
Teams that ran better than their opponent won about 52 percent of the time overall (slightly better than a coin flip) -- with a HUGE SWING coming whether they passed the ball better (.799) or passed the ball worse (.221) than their opponent.
Those percentages are nearly the same every year. Passing better than your opponent is how you almost always win in the NFL. And let's not forget, in our past 38 games, the team that has passed better is 37-1 (with the only loss coming on a last-minute TD). The team that has rushed better is 19-19.
You lose.