You can improv D&D, even 100% if you really want to. Due to life responsibilities, I don't have time to do a lot of prep, so my games are usually 60-70% improv. Most of my prep goes into NPCs, dungeon maps if they are going to one, and plot points that may or may not happen, depending on how things play out. The rest is improv.
I tend to be of the opinion that the actual game is not the rules of the game, but what happens at the table. So if your game is 60-70% improv, then that is what D&D is regardless of what the text says to do or what you think the text says to do. In practice, D&D is mostly improvisational. For D&D to not be mostly improvisational, you need a strong table agreement to stay on the rails. For example, I'm currently taking a break from GMing, and our group is playing a Pathfinder AP with another player putting on the GM hat to let me be a player for a change (the first time I've really gotten a chance to be a player in like 15 years). Because the GM is relatively inexperienced and explicitly has said he's running a Pathfinder AP to minimize preparation, I'm going really easy on him to minimize the amount of prep he needs to do. Even then, it's probably 10-20% improvisational, and the GM is learning just how little an AP really gives you and how much preparation it would take to really run it well.
When I look at something like FATE, I see a game that tells you on paper that you should be mostly (but not completely) improvising, and I really wonder how it plays. From what I've seen of it, it plays terribly. An example in the public domain is Wil Wheaton playing FATE CORE w/ Felicia Day, John Rogers, & Ryan Macklin on 'Geek and Sundry', which struck me as a total train wreck of a game with emergent play that looked nothing like the presumed goals of the game's designer - despite the fact that Ryan Macklin was the one running the game.
Ever since reading the original VtM gamebook, I've been struck by how different the game as described in the rules can be from the game created by the rules. For example, the game described by the rules of VtM was a game for two people in which one person explored their inner monster, with an end state of either the monster winning or perhaps being vanquished. But the game created by the rules was nothing like that at all, and was as far as I can tell rarely if ever played according to the examples of play in the text not only because most RPG groups aren't two people, but because the rules didn't push the game heavily in the described direction. Fast forward a bit, and this became one of the things Ron Edward at The Forge would repeatedly pound on, and became a big part of the basis of his 'system matters' theories - how to create games that actually created the game they described. One of the theories that came out of that is what Ovinomancer is calling, "Story Now", but then for me the questions are, "Is something like FATE actually Story Now in any really meaningful way, and does it actually produce Story Now play in practice?", and more to the point, does "Story Now" really make for better stories that engage with narrative more productively than more traditional styles of play?
Which brings me back to the claim that is really in dispute: when deciding on the story, should we take the character of an NPC as input into the resolution mechanic of some sort of player driven persuasion challenge, or should the character of the NPC entirely fall out from the persuasion resolution challenge? Which has priority - the fiction or the mechanics? When we start the play loop and we are wanting to generate 'story now' in a satisfying manner, what do we start from? Fiction, and then use mechanics to arbitrate the unknowns, or mechanics, and then use fiction to arbitrate the unknowns?