Here are some of the key passages in the 4e DMG about saying yes and trying not to say no:
As often as possible, take what the players give you and build on it. If they do something unexpected, run with it. Take it and weave it back into your story without railroading them into a fixed plotline.
For example, your characters are searching for a lich who has been sending wave after wave of minions at them. One of the players asks if the town they are in has a guild of wizards or some other place where wizards might gather. The reasoning goes that such a place would have records or histories that mention this lich’s activities in the past, when the lich was still a living wizard. That wasn’t a possibility you’d anticipated, and you don’t have anything prepared for it.
Many DMs, at this point, would say, “No, there’s no wizards’ guild here.”
What a loss! The players end up frustrated, trying to come up with some other course of action. Even worse, you’ve set limits to your own campaign. You’ve decided that this particular town has no association of wizards, which could serve as a great adventure hook later in your campaign.
When you say yes, you open more possibilities. Imagine you say there is a wizards’ guild. You can select wizards’ names from your prepared lists. You could pull together a skill challenge encounter you have half-prepared and set it up as the encounter that the PCs need to overcome in order to gain access to the wizards’ records. You could use a mini-dungeon map to depict the wizards’ library if the PCs decide to sneak in, and then scrape together an encounter with a golem or some other guardian. Take a look at your campaign lists, think about what would help the PCs find the lich, and tell the players they find that information after much digging through the wizards’ records.
Instead of cutting off possibilities, you’ve made your campaign richer, and instead of frustrating your players, you’ve rewarded them for thinking in creative and unexpected ways. (pp 28-9)
Thinking players are engaged players. In skill challenges, players will come up with uses for skills that you didn’t expect to play a role. Try not to say no. . . . However, it’s particularly important to make sure these checks are grounded in actions that make sense in the adventure and the situation. If a player asks, “Can I use Diplomacy?” you should ask what exactly the character might be doing to help the party survive in the uninhabited sandy wastes by using that skill. Don’t say no too often, but don’t say yes if it doesn’t make sense in the context of the challenge. (p 75)
Sometimes the best or the most fun ideas for countering a trap or hazard come as a flash of inspiration during play.
Remember the first rule of improvisation: Try not to say no. When a player suggests a plausible countermeasure for a trap, even if that possibility isn’t included in the trap’s presentation, figure out the best way to resolve that using the rules: a skill check or ability check against an appropriate DC, an attack, or the use of a power. You can always use the DCs that are included in the trap’s description as example DCs for using other skills and abilities. (p 86)
You should allow and even encourage players to come up with their own quests that are tied to their individual goals or specific circumstances in the adventure. Evaluate the proposed quest and assign it a level. Remember to say yes as often as possible! (p 103)
Once you’ve identified where you want to start your campaign, let the players help tell the story by deciding how their characters got there. . . . This step is one of your best opportunities to get the players doing some of the work of world design. Listen to their ideas, and say yes if you can. (p 142)
It's not Burning Wheel, but it's not hopeless either. We've got player-authored quests, including inside the context of a bigger adventure/scenario (the wizard example, with the relatively straightforward nature of 4e prep being leveraged). We've got player participation in setting/start-up. And we've got glosses on p 42 for skill challenges and using skills vs traps and hazards.
It's actually better than I remember!