As others have said, higher octane is less resistant to burning and thus more stable. It is best suited for very high compression (and thus high HP n/a motors) or forced induction, where compression is made higher via boost which comes at the cost of a higher intake air temperature. High octane is needed to remain stable under these more extreme conditions to avoid premature firing in the cylinders (detonation).
Ford says use 87, so use 87 in a stock motor.
At lower altitudes in cold weather it might be okay to use 85, we all know plenty of people who put 85 in thier vehicles and don't have any "problems" where 87 is actually recommended. Ford expclitity says in owners manuals NOT to use 85 at high altitudes. I trust them, they designed the engine.
^ Deuces has a point, the main thing that a "tune" can do on a conventional fuel injected vehicle is change your air/fuel ratio under different conditions. All of us turbo owners know that detonation is occurs usually during a lean mixture, so I'd say it's plenty logical that a different tune could be suited for a higher octane.