Earlier quoted context omitted.
As far as I've found, I can't make my iPhone not make the low-battery sound.
The iPhone does not play a low-battery sound when the mute switch is on. The only sound that plays is sound that you specifically asked for, like music or sound from a video, the alarm and sound from badly behaving apps.
The problem I described happened many times these last 6 days. I made extra sure it was on silent each time (it was). I was pretty sure anyhow since I pretty much perpetually leave it on silent.
Maybe it's a quirk of this particular model (iPhone 5), or some sort of bug, but it's definitely making the low battery sound while physical switch is set to mute.