Is this true?

[Unit 5302]

Octane rating tells you how long the fuel will burn.

In a high compression engine, you need a slow burning fuel that won't detonate. In that instance you sacrifice a little power by going to a higher octane fuel, but that power loss is insignificant to the power loss you'd experience from the mis-firing of the cylinder.

For an engine that doesn't need the higher octane fuel, all you're doing is slowing the combustion process, and weakening the cylinder pressure because it's slowing the expansion from the burn. Since cylinder pressure is one of the main contributors to torque, it also directly effects the horsepower production from the engine.