That depends on the system.
In AW, as per what I posted just upthread of this, one of the principles is for the GM to say what their prep demands, and to treat it as binding. The point of this principle, as I understand it, is to help ensure that "the unwelcome and unwanted" (terms used by Baker, as per the OP of the current "rules " thread that you've participated in) become part of play. The GM is not permitted to wimp out and change things.
Really? Because I'm looking at Apocalypse World right now, and under MC Agenda, it says, "Everything you say, you should do it to accomplish these three, and no other. It’s not, for instance, your agenda to make the players lose, or to deny them what they want, or to punish them, or to control them, or to get them through your pre-planned storyline
(DO NOT pre-plan a storyline, and I’m not <expletive deleted> around)."
(Emphasis mine.)
In Monster of the Week, the book says, "Ask questions and build on the answers" and "You don’t always have to decide what happens."
In Masks, the book says, "You don’t know exactly what will happen over the course of the game. You don’t know who the PCs will become. You don’t know how they’ll change the city. That’s why you’re playing in the first place—because you’re excited to find out! MASKS is a game about change, about young people growing up, about the city reacting and reshaping itself in response to the people within it. Don’t plan on any single course of events coming true—plan only on pushing and prodding the characters and the setting to see what it might become."
In Root, the book says, "Imagine how you would tell a story about something that happened to you in your real life. At the time that the story is happening, you have no idea what exactly will happen next! When it’s all said and done, you can look back on the events, fit them together, and make a real coherent story out of them, but in the moment, who knows what will happen! It’s a bit like that when you’re playing Root: The RPG with the other players, rolling dice and describing what happens: you’re “in the moment” and unsure of what will happen. After the fact, you can look back and fit things together as a coherent story, seemingly planned the whole while…but in the moment? Who knows what will happen! The game will be infinitely stronger if you let yourself be surprised by it, by what the players and characters do, by how the dice roll, and by what happens next. As the GM, you are always trying to be excited about a story whose ultimate outcome and events you don’t know."
In Dungeon World, the book says, "This is how you play to find out what happens. You’re sharing in the fun of finding out how the characters react to and change the world you’re portraying. You’re all participants in a great adventure that’s unfolding. So really, don’t plan too hard. The rules of the game will fight you. It’s fun to see how things unfold, trust us."
So where on
earth are you getting the idea that in Apocalypse World, or in PbtA games in general, that the GM can't change things?