Octane has nothing to do with injectors, the injectors have no idea what octane fuel is passing through them.
Octane's sole purpose is to control the gasoline's burn rate and how much compression it can withstand before self-detonating from excessive compression. Octane itself does not add power to gasoline, neither does it help the engine run cleaner. High compression engines require more octane because they compress the fuel more, so more octane is needed to prevent the gasoline from prematurely igniting on its own from the high performance engine's extra-high compression ratio. Premature ignition is what causes the pinging or knocking that is audible when running the engine under a heavy load or if you're running too low of an octane for the engine's design.
In fact, the higher the octane, the more difficult it is to ignite and the slower it burns. In fact, running too high of an octane in an engine can conceivably leave deposits behind.
The only time an engine designed for 87 octane will require a higher octane is when something is wrong with the engine and a higher octane is required to get rid of pinging. That is usually from nothing more than a heavy load of carbon that has built up inside the combustion chambers... which is usually caused by driving the engine too conservatively. Excessive carbon can often be "blown" out of a carboned-up engine by driving extra aggressively for a few days. I.E. accelerating hard to high RPMs which will often burn off/blow out the carbon that has been allowed to accumulate inside the combustion chambers.
If your engine was designed for 87 octane and it isn't pinging, then there is absolutely no... none, zero, nada, benefit to running a higher octane. It won't run any better or faster, nor will it get better mileage.
The only benefit seen by running higher-than-required octane fuel is that the gas station and gasoline manufacturer made a little more $$$ off of you than they deserved.
One more thing... a gallon of 87 octane gasoline has exactly the same energy content as a gallon of 93 octane gasoline. Again, octane is not power, it only helps the gasoline withstand being compressed without igniting prematurely from the compression of the air fuel mixture.
Your buddy is just part of the majority of people that have no real idea what octane is and what its purpose is.