This is true, but there is a bit more to the story.
It is true that "octane" is NOT "power". In fact, the opposite is true. A gallon of high-octane fuel has a few thousand less BTUs than "regular" lower-octane fuel. The octane is only a measure of resistance to detonation, usually due to the higher heat of a higher-compression engine.
If, ... IF you have a high-compression engine that DOES require higher octane fuel, that is great. Most of the computer-controlled, fuel-injected engines in vehicles nowadays have some protection features that will detune the engine if knocking or pinging is detected due to lower-octane fuel. That detuning WILL lower the performance of the engine.
If that lower-performance engine is all you have ever experienced, then you add the proper fuel, which allows the engine to operate at full performance, you can certainly get the impression that "higher octane gave me better performance".
Just got our Spyder this past weekend, have not had to add any gas to it yet. Also, still getting used to the handling, have not had a chance to explore the limits of the engine performance, so I have absolutely nothing to compare to, so I don't know the difference.
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