More nuance is required.
For exploration it's not sufficient that a player authors fiction - he must author the fiction in specific ways and about specific things. Authoring fiction outside of those specific ways and specific things can/will conflict with the intended purpose of exploration.
For example (starting with baby steps): if a player pre-authors all the details about a town and it's inhabitants, then he literally can't explore it because he already knows what's in that town. He could say his character has never been there and then have his character explore it, but that's not the player exploring the town.
Yes. But not any fictional action can be declared and still be exploration. Some actions preclude exploration. An example: declaring your PC remembers he's been to this location before and knows who and where everything is.
So, in terms of exploration, having played Dungeon World quite a lot where there's intended to be a certain degree of player agency WRT what the story focuses on, the pedigree of the fiction is much more complex than 'player makes up a town'. This is intentional and is a product of good iterative game design, just like the B/X D&D exploration rules are a good intentional product of iterative design.
For instance: players pretty much never author fiction directly, except about their own PC, and then in a very limited fashion. So a GM might ask "where are you right now?" at the start of scene 1 of the first session of play. One of the player's might respond "we are in the market place of Townville at noon on Wednesday, market day!" Now, the GM is going to accept this, but it hardly constrains the nature or state of the town, or even the actual situation the PCs are in. The GM might consult his notes and see that the Fighter is 'Good: Defend those weaker than you' and respond with "You notice what appear to be some town watchmen beating a much smaller person with their truncheons in a nearby alley." Everyone is exploring the setting, the GM is presenting situations that feed off the PC's avowed traits (not yet proven, but asserted on the character sheets). The players assert PC actions in response which refine those avowals and lead to further exploration.
The fighter approaches the alley boldly with the idea of defending the weak. The GM asks him what he does, and he responds "I call out the watchmen and demand that they halt their actions." The GM decides to use Defy Danger +CHA here, as the situation is potentially hazardous and Parley doesn't (yet) seem to apply. The player rolls 10+ and asserts "Jorge sees that one of the watchmen is a guy he warned off last week for trying to extort money from his cousin. I glare at him and he urges the other's to back down, successfully." Now there's a ton of possible directions for things to go, Jorge the Fighter might now Parley (he's got something on one of the watchmen) or the GM could switch to using the 'victim' as a way to put some pressure on things. Maybe the youngster signals the party Thief in Cant, telling him to make a distraction so a brother can bug out. "How does this kid know you're a thief?"
And on and on and on, there's so much exploration going on here! And you can see how the combinations of questions, low myth, ability to describe success (within reason), GM moves altering focus and generating pressure to move the story along, and simple cooperative fiction authoring works really well and produces a feeling of learning and exploring within the milieu. IME this all feels quite natural. Remember, DW is also very insistent on things being described from a character PoV, using character names, etc. at all times. It is all deliberate! If you exactly follow the game's instructions things work REALLY WELL and exploration is very much alive. Obviously, with experience, you can develop additional techniques and do more specific things, but OOTB the whole "everyone at the table with equal agency" does work. As for disputes, DW recommends they be addressed by the table if they arise. IME it is not common and usually GMs are competent to address any issue, much like other types of play.