Just a few points
1)almost all electronic filtering devices require a good ground to accomplish any filtering.

2) most cheap UPS units only provide power when the power is off, the rest of the time the power supplied is directly from the incoming line. Better units(on-line UPS's) the power is supplied from the inverter at all times.

3)The braided covering on the coaxial cable is a shield, if it is not properly grounded it becomes an antenna the picks up broadcasted signals from the air and outputs it as voltage.