The connection between game mechanics and events in the game world is derived / imposed meaning.
Put simply, there is no sense in which the Nobilis rules---or even the Amber rules---are more loose than HERO's. Further, in neither case is there any simulation. There is simply a set of conventions by which we convert mechanical outcomes into meanings, and vice versa, that may yield a single reasonable meaning, a choice of many reasonable meanings, or a vague/difficult meaning, depending on the situation and the game.
Strict systems are not more mechanically strict; rather, they sacrifice plenitude of possible meanings to avoid the vague/difficult cases. Loose systems, conversely, risk vague/difficult cases in order to ensure a broad enough selection of meanings to inspire and empower.
(I don't think either is inherently better, although quality varies hugely within each paradigm.)
The ultimate loose system is the "1" system. The rule is simple: when characters act, the result is 1, and the GM determines what that means.
The ultimate strict system is the Reality System. Whatever you do as a player is what your character does, and the players work together to determine what that means.