You are correct. I was wondering about leaving the charger plugged in after I remove the batteries.
Just wanted to make sure. If it makes you feel more comfortable to unplug your charger when not in use, then do so. I do not unplug mine nor do I unplug other electronics such as my computer, TV or even my stereo which generates a
load more power than a small battery charger. However, I will never dispute those who may have legit reasons, such as concerns of an electrical short causing a fire. We do what makes us feel more comfortable and that can’t be disputed
Will say though, your UPS is also an electronic device that carriers even more of a risk given it also has a volatile battery that is under constant charge while the power is on. I have dealt with UPS failures and they are not nice.
Any piece of electronics can fail and cause a fire. I had a 200 watt power amplifier fail and burn 3 foot hole in my carpet. Ironically, the name of the amplifier was called Ampzilla.