For me, the center of the "school argument" is over what the guy behind the screen is doing. Rather than introduce the positions myself, let's take a quote from the 4e DMG:
"When you start a campaign, you should have some idea of its end and how the characters will get there. Fundamentally, the story is what the characters do over the course of the campaign.
Keep that point in mind—the story is theirs, not yours... If the characters go in drastically unexpected directions, try to coax them back to the story you want your game to tell without railroading them." (Emphasis mine.)
This is what one might call "shame-faced" storytelling. The DM is telling the story - but has to remember it's the characters' story, not his! The DM should try to get the characters onto the story he wants to tell - but don't "railroad" them!
Paizo's Gamemastery Guide has the courage of its convictions:
"Storyteller: Weaving plots involving the characters and any number of nonplayer characters, leading dialogue, and unfurling a vast tapestry of ideas, stories, and adventure, the Game Master is a storyteller first and foremost. While the game is a collaborative narrative told from all sides of the table, the Game Master paves and maintains the road along which the adventurers walk." (Emphasis mine.)
It would have been a step too far to literally say that the characters should be "railroaded", but it's quite clear what this means.
On the other side, the 1e DMG:
"It is no exaggeration to state that the fantasy world builds itself, almost as if the milieu actually takes on a life and reality of its own. This is not to say that an occult power takes over. It is simply that the interaction of judge and players shapes the bare bones of the initial creation into something far larger... What this all boils down to is that once the campaign is set in motion, you will become more of a recorder of events, while the milieu seemingly charts its own course!" (Emphasis mine.)
The reader, naturally, will be able to tell which side I'm taking. But the main point I'm trying to make is that there is a real debate, over something fairly important to the hobby.
Under these definitions, a GM who gets a group together with the intention of playing G1-3 seems to be engaging in "New School" play. I do not find that a convincing argument. I'm not a fan of 'story-telling' GMs, but I'm not sure that it's a valid way to distinguish between old- and new-school gaming styles even if you're restricting the argument to just D&D. Note that plenty of modern games are far more inclined to suggest a play style recognisable from the 1e DMG.