Dirty Fate? Dirty Monster Hunting?

John Wick's Dirty Dungeon

Each player adds elements to the dungeon by describing how they learned about this element - dungeon survivors, old maps, books, whatever. Each time they add something to the dungeon, a d4 is added to the pot. In the dungeon, players may take out a d4 whenever and add it to a die roll.

While the players are adding to the dungeon, the DM gets a bead every 10 minutes (or whatever time period you like).

Everything the players state is true.

The DM may spend a bead during play to make any player statement false.

So, basically, the players build the dungeon from the ground up, and then adventure through it. However, because the DM can change elements at any point in time, their plans are not foolproof.

Any ideas how to apply this to Fate or FAE? Maybe as a "Heist" game?

Or maybe Monster-of-the Week?