Magic games are a mixture of game states interspersed with event occurences.

We can derive this from rules 700.1 and 613.

Now when Miracle was initially released it played a bit fast and loose with the rules, but arguably fit within the framework.

"Miracle [cost]" means "You may reveal this card from your hand as you draw it if it's the first card you've drawn this turn. When you reveal this card this way, you may cast it by paying [cost] rather than its mana cost."

So you reveal the card from your hand "as" you draw it, ie. while the draw event is occurring.
Now generally something that has something occur while something else is happening is typically a replacement effect applied to the event before the occurrence.
Is it conceivable that Miracle is generating a replacement effect with a nested trigger?

Arguably, yes.
Is there anything in the rules that could support this interpretation? Yes.

400.6. If an object would move from one zone to another, determine what event is moving the object. If the object is moving to a public zone and its owner will be able to look at it in that zone, its owner looks at it to see if it has any abilities that would affect the move. If the object is moving to the battlefield, each other player who will be able to look at it in that zone does so. Then any appropriate replacement effects, whether they come from that object or from elsewhere, are applied to that event. If any effects or rules try to do two or more contradictory or mutually exclusive things to a particular object, that object's controller--or its owner if it has no controller--chooses which effect to apply, and what that effect does. (Note that multiple instances of the same thing may be mutually exclusive; for example, two simultaneous "destroy" effects.) Then the event moves the object.

603.10. Normally, objects that exist immediately after an event are checked to see if the event matched any trigger conditions, and continuous effects that exist at that time are used to determine what the trigger conditions are and what the objects involved in the event look like. However, some triggered abilities are exceptions to this rule; the game "looks back in time" to determine if those abilities trigger, using the existence of those abilities and the appearance of objects immediately prior to the event. 

Now neither of these two rules is 100% applicable to our drawing a card with Miracle situation, but the underlying principles within them if extended could make Miracle work for a card that has Miracle printed on it. Miracle is essentially a replacement effect that you applied to the draw event without knowing you applied it as the draw was happening. Similar to how a retro trigger works, it had the ability before the event occurred so could apply it to mod it as it occurred.

Miracle is essentially a new kind of "retro" replacement effect paralleling the two types of triggered abilities (normal & retro).

Now, what's the issue with Aminatou, Lorehold, and Miracle Man then?

They give the drawn card Miracle as a Layer 6 continuous effect in the game state following the draw occurrence, after it has occurred.
To mod the draw event with the reveal, it needed to have Miracle before the draw occurred and it didn't have it at that point.

Now no one is going to argue that their abilities don't function as we expect them to because afterall Wizards doesn't print cards that don't function.
The issue is with the rules because as they are currently, Miracle granted to a card in hand by a continuous effect doesn't function in the framework.

A simple solution would be to add a rule to 702.94

 702.94c A continous effect that grants a card in hand Miracle also grants it to the card that it was in the library.

This would make it work as expected in the rules framework. It had the ability in the library to let you reveal it if desired, no different than a card with Miracle printed on it.

Edited Todd Bussey (Today 07:55:52 AM)