Ungrounded outlet indicates grounded when an UPS is plugged in
The cheapie 3-light testers work by connecting 3 lamps in a triangle fashion across the 3 outlet pins.   The hot-neutral lamp works in the obvious way.  The hot-ground lamp works if the ground pin can find a path back to neutral, presumably via a ground wire correctly bonded to neutral in the panel.  But not necessarily.

It sounds like the UPS is connecting neutral to ground in some way.  Perhaps with its own onboard ground tester. 

All of this is idle amusement.  If you know there's no ground wire, then that's your answer - the tester's output is irrelevant.  These testers are a little bit hokey and are not the last word on the subject.