Since I began playing in 1983, the vast majority of DMs have been some degree of the synthesis of the two methods. I have encountered very few of the "Story Before as pictionary" that you describe, and those have been railroad DMs.
I think that most traditional play, at least after the game evolved past being primarily dungeon exploration(basic D&D), has been that blend of the two methods.
That's where I think the disconnect comes in and most of the disagreement with the portrayal of the traditional DM comes in. You guys are describing it in the context of a railroad(Story Before as Pictionary) and we're like, "But wait. That's not how it plays out."
Gotcha.
So let me be clear for everyone conversing and everyone reading along.
When I'm talking about Story Before and comparing it to Pictionary, I'm not talking about any person's specific play (eg Maxperson's). I couldn't say what is happening at your table (or CL's or SC's). It sounds to me that you guys tables experience significant drift in the course of play. I can't tell when/how/why that happens (I can tell if I'm beholding the game or reading robust play excerpts...but not through just conversation) in the course of your play, but that appears to be the play that you guys are representing.
When I talk about Story Before and compare it to Pictionary, I'm talking about my own RC Hexcrawls and my own Moldvay Dungeon Crawls. Outside of Reaction Rolls, Morale, and Wandering Monsters "hitting" (which have an element of procedural Story Now to them), those games are 100 % Story Before kindred to Pictionary:
1) I pregenerate a ton of map and key and themed (not themed as it pertains to the PC...generically themed w/ D&D's tropes) content.
2) I (effectively), to borrow PBtA parlance, make (hopefully) deft soft moves to telegraph threats/downstream content inherent to (1) in order to (a) pique interest/provoke and (b) flag elements of danger (type, scale, nature, etc).
3) Players explore it using the rules and procedures of play to draw inferences, deploy guile and gambits, solve puzzles and defeat obstacles; play skillfully (or fail to do so and suffer the consequences).
4) Rinse/repeat 2 and 3 until all aspects of play are resolved (with the game coming to an end).
So this isn't a value judgement. I'm just describing a healthy phenomenon (in particular, the majority of my D&D play...all of it, in fact from 1984 until late 90s) inherent to D&D play. Pictionary isn't doing negative connotation work here. In fact, IMO, to call something Pictionary - eg a very well put together game - is to call it
a well put together game!