Ah, but that's not the case.
They're not rejecting the concept of a DM in the least. They need someone to provide the game world, the backdrop, the history, to referee the game, to provide opposition, and to adjudicate and narrate the results of what they do. And then they just want her to mostly get out of the way while they explore the game world she's provided and - as they go - find and develop (or create) their own adventure hooks leading to adventures leading to stories that become the campaign. The DM here has to be more reactive than proactive; instead of proactively putting out hooks and bait she tells them about their surroundings and then sits back and reacts to what the players and characters do.
Frankly, I question how possible this is. We saw the horrible flop that was No Mans Sky precisely because the "DM" has provided a vast, theoretically endless world to explore, but filled it with nothing but random wandering monsters. And that is a multi-million-dollar computer game developed over several years by multiple people. DMs have to put
something in their world and there's no guarantee that
any of it will entice the players. So, unless the players themselves are adding things to the world, I don't see how a DM can actually do what you are suggesting. Eventually "reactive"
must become proactive because a series of events
must lead to
some kind of conclusion. You find a Prince lost in the woods (who
must by nature of being a Prince, belong to or be related to a King, a Queen, a country, it's people, and so forth, and all of those things
must exist in order for the Prince to exist.) Right here is the defining moment where a DM
cannot be reactive. Sure, they can say "oh yeah, Princeling has a quest for you."
But, and this is speaking from experience, "on the fly" DMing can only get you so far. It only goes so deep (and usually only just past your ankles). But the more the players go down that rabbit hole, the more the DM
must become proactive instead of reactive. That Prince means the DM must now create a King, a Queen, a nation (past, present or future or even otherworldly!) but now it
must exist. That means names, places, descriptions, inhabitants that
must be created. We're well past "reactive" DMing here and deep into the territory of proactive DMing.
And I sort of wonder whether this is somewhat the case in the OP; that the DM might want to step back a bit, take a reactive stance for a while and see what the players and characters do. If they do nothing then he's well within his rights to boot them into action somehow (and at this point the players have no legitimate right to complain if he does), but if they do something then he can run with it and see where it goes.
Lanefan
Speaking from personal experience, every time I have veered off from the "interesting things I have created" into the "random whatevers the players want to do" my games have wholly collapsed. Which is why I don't do this anymore, and I wouldn't advise it to
anyone who didn't have a fairly massive sandbox world to play with (even if it's someone else's world they're running). Inevitably the players chew through content faster than the DM can create it and the content gets inevitably shallower as this goes on.
Being reactive takes an entirely different skillset than being proactive. An entirely different way of thinking. It's not something a lot of people can simply "switch" over to.