Read another article (American Car and Driver I think). Couple of caveats first. Its US fuel (if you can call it that), and they seemed interested in power only and don't mention or test mpg.
The key points, firstly regarding engines designed to be able to run on "regular" (which for Americans seems to be 85-87

) as opposed to "premium" (which is a measly 91!):
in some engines designed for regular fuel, you can advance the timing if you burn premium, but whether this will yield additional power varies from engine to engine.
Regarding how the engine sensors detect the octane:
Relying on these sensors, the engine controller can keep each cylinder's spark timing advanced right to the hairy edge of knock, providing peak efficiency on any fuel
...
only a few vehicles calibrated for regular fuel can advance timing beyond their nominal ideal setting when burning premium.
And their track and road testing results:
Our tests confirm that for most cars there is no compelling reason to buy more expensive fuel than the factory recommends, as any performance gain realized will surely be far less than the percentage hike in price.
So still inconclusive. Regarding power (with sh!tty US fuel and presumably engines that expect it) you don't get any gains in non performance or in older tech cars. No tests were done on something similar to the GTI though.
Regarding the science, it seems to me that technically the GTI engine can make use of the higher octane fuel, but again any power or mpg (or cleaning) improvements are unproven and even if they exist do they cover the higher fuel cost? We just don't know.
EDIT:
Also does anyone know how the hell they get away with 91 in the US? Their premium is significantly worse than the worst EU fuel. Seems mad. Also makes it hard to get decent info because I'm actually highly sceptical about how much of this will apply to our situation.