Alarm not triggered when battery low (but also when battery full)

I've noticed that on my Android 4.3 Samsung Galaxy SIII, as well as on previous devices, the alarm is not triggered when the battery is low, and any applications that depend on this will thus not be able to produce a sound alarm when set up to do so because they will not receive the signal from the hardware under such circumstances.

Anyone experiencing the same thing? Can anyone please confirm this?

UPDATE:

There have also been several occasions (perhaps up to 10%) of the time, when the battery is full and the phone is connected to the computer, but when the timer expires the timer just won't ring. I've experienced this both on the SIII as well as on an older android phone I had purchased previously. Can anyone explain the reason for this?