Let's not forget that the PCs can make decisions too.
Suppose we evolve Celebrim's world's simplest RPG system in which all propositions are resolved by coin flips into something resembling a rules light system.
That system would have at its mechanical core something like:
If the proposition is deemed by the GM impossible, it fails.
If the proposition is deemed by the GM to have no risk, it succeeds.
Otherwise, flip a coin and have the GM narrate what he believes is an appropriate success result on heads and an appropriate failure result on test.
If you compare that to a typical rules heavy system then for a particular task it will say something like,
"A characters running jump is equal to their strength score minus their encumbrance modifier in feet. If a character is willing to land prone they can add half their height to the jump distance. If a character makes an easy athletics check they can add 1d4 feet to the distance jumped. The test must be made after they have committed to the jump but before the jump is resolved. If the test fails they jump their normal distance. If a moderate athletics check is attempted, then add 2d4 feet to the jump distance but on a failed check no extra distance is obtained and a muscle is strained and they take 1d3 strength damage unless they make a moderate stamina check."
And we would expect similar detail for scores of different potential tasks.
As a player, compare which one gives you greater understanding and control over the stakes? Which one gives more authority and latitude to the GM? As a player which one gives you more ability to plan for the outcome of a roll and more confidence you won't be cheated on a whim?
So, the rules hold the authority, or the rules are granular?
Almost as a tautology, both. The more the rules tell you how to resolve a situation, the more authority they have and the less authority the referee has. The more the rules lean on the GMs judgment and the less specific things that they tell you, the more empowered the GM tends to be.
Now, you can of course compensate for this by for example having narrative currency and fortune in the end with stake bidding or negotiating phases if your goal is to have a rules light system where narrative authority is shared. But that act of stake sharing itself is going to complicate up the system especially if by "system" we mean "all the processes of play".