LSSpam
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The Gulf Coast offense proves this to be myth. This isn't the NFL ten years ago...
More like 35 years ago.
"The run sets up the pass" is an adage from the days of most of your pass production coming from a play-action into a 7-step drop where your quarterback looks down the field at vertical routes. Bill Walsh obsoleted that as the dominate passing philosophy in the NFL.
Philosophically, offense in the NFL is about increasing "frontage" (to get military on you), that is to say, the volume of space a given number of men have to cover. i.e. "Spreading the field out".
One way of doing that is, in fact, through the play-action pass and a strong vertical passing game. It pushes defensive backs away from the LOS and therefore increases.
Spread offensive elements, etc simply do the same concept in a different manner. They spread the field horizontally. By putting 3 or 4 receivers near the LOS and out wide you draw the defense taut at the LOS, but spread out. There are many other concepts which can accomplish the same thing, pitch plays, swing passes, etc.
When you introduce what we would think of (somewhat incorrectly, but we'll use the term anyways) as "West Coast" style routes, shallow routes timed with the QB dropback, and combine that with a spread formation, you get vertical depth too. If Devery Henderson beats his man badly on a quick slant, he can go the distance, requiring safety depth (think the 99/00 Rams with Hakim, Bruce, and Holt).
Of course the defense can flip the script some. One of the problems with spread formations is it allows the defense to proactively gain a "frontage advantage" directly in front of the quarterback through blitzs. It exposes them deep and on the edges, but they can seriously disrupt the quarterback.
Offenses can respond however with things like misdirection, screens, short drop backs, shotgun formations, etc, etc
Well the whole point of all of this is that football is way to complex and evolved to be reduced to such an uninformative and simplistic adage like "the run sets up the pass". We're way beyond that point.