I've had the pleasure of being in sessions P-cat has run, and I think I understand what you're getting at.
In the various factional head-buttings, much has been made of how "storytelling" is bad, focusing on how the GM is railroading a particular plot. And while there are some GMs who do that, by and large, that's not what storytelling in RPGs is about - as you've seen.
A storytelling GM is one who gives the needs of story high priority. And by needs of story, I mean things like evocative description, theme, and dramatic timing. There are in the world still a few people around who tell stories professionally. They do it well enough to get paid, and they have techniques to keep the audience engaged - tricks of body posture and vocal control, for example. A GM can use some of those same techniques at the table, without predetermining the plot.
Many GM's go by the "if everyone seems entertained, I'll let them keep going" philosophy. This GM will allow you to spend a half-hour of your game debating how to do down the mineshaft, so long as nobody's there twiddling their thumbs.
The Storytelling GM knows that if you wrote this half-hour down as a story, it'd be pretty boring. Even if everyone is engaged and interested in the debate at the time, afterward nobody's going to care - when they tell the war story of the session, it'll be summarized as, "We spent a half-hour debating how we'd go down the mine, and then we...." The Storytelling GM sees that half-hour as flaccid dramatic timing. Unless something else cool is going on between the party members such that the players will remember it, the Storytelling GM is going to try to urge the players on to some action.
umbran nails it right there. It's not about old-school/new school. Its making your game interesting, rather than slow and boring. His points are valid whether you're on a sandbox, or adventure path.
For a "storytelling" dm, the intent should be "how do I keep them moving towards THEIR goal in a dramatic way that THEY will enjoy". As opposed to "how do I keep them moving towards MY goal that follows MY story".
If it is considered a valid technique for a lean-back DM to "figure out how to mess with and complicate the players plan", then it is equally valid for the lean-forward DM to "figure out how to keep them moving, so they don't dither or wallow in awkward moments"
Having that sense of urgency helps. It's a key part of how I run faster combats. Just within the combat framework, you can do things to make the players feel tense and rushed. Its a style of running the combat, not tied to specific game rules.
Having that sense of urgency outside of combat helps keep the party moving toward their goal. Either a time-limit by way of "if we don't solve this by noon, bad stuf happens", or by virtued of "if we sit here planning how to get into the mine too long, guards will find us"
Making role-playing scenes move smoothly, so it doesn't feel awkward is actually the harder part, in my mind. I don't want such scenes to play out as DM monologue, but in the same vein, the players don't want to flounder in trying to achieve their social goal.
As I see it though, the key for the DM is to try to make each scene seem cool and to flow with the last scene, minimizing the awkward moments. That idea should be applicable to any game, regardles of how it was planned out.