You understand correctly. It is the fact that the PC, UPS, TV or battery charger, etc, is plugged into the same circuit or near circuit. I saw a major improvement in my situation when I put the PC devices and UPS on the same FilterLinc (used a 10 amp version to be sure I had plenty of reserve). Not all the PC devices are powered directly from the UPS. A printer, an old external dial modem I use for backup to DSL, a flat bed scanner are all on the same FilterLinc but not powered from the UPS itself. By unplugging devices I also found the TV in the same room with the PC was also causing problems. It is a newer flat screen model. Not as severe a problem as the UPS/PC combination but I did get another small bump in reliability when I put that TV on a FilterLinc. I eventually put a FilterLinc on another TV in an adjacent room. When I ordered that FilterLinc I ordered a few spares in case I find something else. Because you see improvements when you unplug a problem device it is a pretty easy diagnostic approach. You might unplug all the potential problem devices and see what you have. Then plug them back in one at a time until reliability degrades. The PC is a problem because you can’t unplug it and still interact with the EZSrve. That is why folks suggested using an extension cord to move the EZSrve away from the PC. It was something I read probably on the Smarthome forum. I believe the first time I saw the extension cord suggestion was in connection with a PLC plugged into the same outlet as the PC/UPS. Same situation, a PLC is connected back to the PC with a USB connection so it is hard to move it too from the PC.
EDIT: I don’t want to rain on the parade but there have been rare cases of hard wired Insteon devices going bad and causing reliability problems. Have seen this documented only a few times. The problem device was found by pulling the air gap switches on a group of Insteon devices and then restoring power one at a time. I would put this on the bottom of possibilities.