I think this completely misses a huge place where players have narrative control in 5e -- spells. Spells are packages of narrative control that players can deploy and the effects happen. The GM is, without blatant and obvious execution of Rule 0 to force their preferred outcome, bound by the effects of the spell. Some spells have grey areas, or require negotiation between player and GM on outcomes, but the effects of the spell are still binding on the GM as far as narrating outcomes go. This seems to get overlooked in discussions of authorities in D&D. I'm not sure why.
I'm not sure spells are all that special of a case, compared to any other character ability.
The player decides what the character's choices are (they choose to cast
fireball) - the dm decides what that means in the narrative. If it's an anti-magic zone, it means one thing, in a dry forest it means something else... but the dm has final say. The player can't tell the dm that the anti-magic zone isn't there, and that the description in the PHB is to be followed regardless of the fiction. The player has control over the decision (the dm can't tell you what spell you cast), but the results of the act of casting are technically/ultimately under the dm's authority.
But unless there's a reason otherwise, the character's decision to cast
fireball, presuming that's a thing the character knows how to do, should almost always result in a ball of fire, at least. Technically the dm can say no, although most of us would expect that a dm who say no to your spell has a good reason for that.
But it's also true that the original breakdown of the play loop left out an important point in step 3: this decision (by the dm) is assumed to follow the agreed-upon rules for that table, whether that means RAW or something else. It's kind of a big thing to gloss over, methinks.
At least, that's how I've always played DnD.