The lamp which stays lit is the "power" lamp, indicating that the device is receiving power. It's not unusual for the "power" lamp to stay lit on USB devices (or to flash on/off in the case of external hard drives) even though the host computer has been shut down. The power lamp on my flatbed scanner also does that, unless I switch off the PSU at the back of my PC like they used to make me do at computer classes (unnecessary in my opinion just for the sake of a few hours, but we had to do it anyway).
Do not regard it as a fault or problem, it's perfectly normal.
Your scanner analogy makes sense to me, so I guess I won't worry about it. Just seems strange to have that light on when the system is off. Thanks.