As already confirmed by everyone else and also your owner's manual, you never ever have to put premium (91 or 93 octane) gasolines in your Coyote GT. Uising 91/93 octane is preferable to achieve the max 420BHP advertised power; going with 89 or 87 octane yields less power because the PCM will automatically retard spark timing.
87 octane is the minimum octane count you can use and no harm will ever happen to your Coyote on 87 octane as long as you have the stock Ford tune or a tune that is designed to operate on 87 octane. The only drawback is on the stock Ford tune, 87 octane only gives you ~405BHP instead of the full 420BHP that you get from 91/93 octane.
Squirrel of Death!
Do not **** off the SoD!!!!