My UPS is an APC--one of the 650 models I think...
As I conjectured earlier, perhaps a rogue frequency is getting into the console--but there is an AC adaptor that goes into the console, which means the adaptor is creating DC, and that the adaptor itself should be able to handle minor AC fluctuations either in voltage or frequency. But, maybe it's a really cheap adaptor, or mine is defective...
Also, as others have pointed out, the UPS should be straight passthrough until a power failure--I think, although I'll have to check mine specifically.
I would fully expect my UPS (as opposed to a very expensive home theater type) to put out a nasty looking AC signal when in backup mode--that's why we have power supplies in computers and such that convert a wide range of AC input to DC output.
Another test would be to plug the adaptor into a non-backup jack in the UPS.
Another issue might be filtering in the UPS. In a past issue of Sound and Vision, a reader was a guinea pig for wi-fi using the house wiring. He found that plugging units into a UPS kept it from working--and in fact the manufacturer warns against it.
So maybe that's more the issue?