Not sure why this feature isn't turned on by default. It would make all the sense in the world. Also not sure why it's hidden and worded so strangely. In any case, I just did this and recommend it. Even if you don't use Siri, it's useful to keep her silent if you don't want her talking to you when you accidentally enable her in a quiet room.
“1. Open Settings and go to “General” then to “Siri”
2. Choose “Voice Feedback” and select “Control with Ring Switch” (yes, the Mute switch on the side of the iPhone and iPad is referred to as the ‘Ring Switch’ here, but it’s the mute button you know and love)”
How to Silence Siri with the Mute Switch on iPhone & iPad | OS X Daily
