The GM has veto authority, and any outcome reached will be one the GM approves. Look at how 5e says it plays, at the core loop of play. All of it is up to the GM. Intentionally. A table can choose to add additional constraints and expectations on how the GM is to use this blanket authority to fiat say what happens, which is great. That was the intent behind this design choice. But arguing that having to have GM agreement for anything to happen is not well described by MMI seems like trying to deny the system design because there's a disliked implication.
The easiest example I can reach for that clearly shows the MMI nature of 5e is the trued and true troll argument. There are multiple answers, but the one that says that the GM tells you what your character can know and do is not wrong according to the system. I don't want to play that way, and don't, but that's me adding addition constraints and expectations to 5e.. And, even here, the general concensus is that this is something GMs can do if GMs want.