I have two comments. The first is--how popular is FKR really and what do its proponents consider the main example of the genre? I've not seen anyone running a game billed as "FKR". I have played a Braunstein, which I see mentioned in the same conversation, but I think there are some key differences. But I won't elaborate on that yet.
Second, the key point I mentioned was "the GM has to make up a procedure" is a fail state. I think that doesn't clash with FKR as you describe it to the extent that the GM has expert knowledge of the material. For example, if I say "my soldiers want to dismantle this barn and use the wood to make a bridge", and the GM did that while in the army, then they aren't really making up a rule, right? They're applying an unwritten rule. In contrast, if I ask "how many bakers are in a town of 10,000", most GMs wouldn't have a solid grounding in demographics and they will have to make something up.
Put another way, we can read the FKR games as having very detailed but hidden rules. The fact that they are 'rules light' on the tin doesn't mean the GM has complete authority to rule however they want. They are ruling in line with their experience, will make the same rulings in the same scenarios, and will make those rulings based on perceived realism. And if the games are really doing what they say they are doing, then two expert GMs should make identical rulings.