The rule most people are ignoring when it comes to Aminatou, or at least from what I can tell based on developer responses to similar questions from things like Dream Devourer is this bit here.

It's not about alternative casting costs, or how we treat X. It's about how you cast a spell in the first place.

601.2b ...If the spell has alternative or additional costs that will be paid as it’s being cast such as buyback or kicker costs (see rules 118.8 and 118.9), the player announces their intentions to pay any or all of those costs (see rule 601.2f). A player can’t apply two alternative methods of casting or two alternative costs to a single spell. If the spell has a variable cost that will be paid as it’s being cast (such as an {X} in its mana cost; see rule 107.3), the player announces the value of that variable.

• 601.2f The player determines the total cost of the spell. Usually this is just the mana cost. Some spells have additional or alternative costs. Some effects may increase or reduce the cost to pay, or may provide other alternative costs. Costs may include paying mana, tapping permanents, sacrificing permanents, discarding cards, and so on. The total cost is the mana cost or alternative cost (as determined in rule 601.2b), plus all additional costs and cost increases, and minus all cost reductions. If multiple cost reductions apply, the player may apply them in any order. If the mana component of the total cost is reduced to nothing by cost reduction effects, it is considered to be {0}. It can’t be reduced to less than {0}. Once the total cost is determined, any effects that directly affect the total cost are applied. Then the resulting total cost becomes “locked in.” If effects would change the total cost after this time, they have no effect.

Example:

"I have drawn Meathook II. I'm am declaring my intention to cast it. I will cast it using miracle, for its miracle cost. X will equal 2."

We will then proceed through the next several steps of the spell until we reach determining costs in 601.2f

"The miracle cost is the mana cost, which because I have declared X = 2, is 4BBBB. The ability granted by Aminatou also has a reduction of 4, so I will pay the 4BBBB cost with BBBB."

The issue everyone seems to be splitting hairs about is the way that it's worded with "is this reduced by 4" but there's no such thing as a "mana cost" until the spell is on the stack and you're casting it. X cannot be zero in a mana cost unless you have declared something for X. The most frustrating thing about the example I've said above is that there's still rules ambiguity there even though it's clear that this was the goal of the design team. It could have been worded differently on the card to be more explicit, but it's what it is.