It would have to have been a surge-protecting power strip? Probably, the MOV's in the surge protector part were interacting with the input circuitry in the UPS. (That alone smacks of bad design, but it's not a huge deal in practice because the UPS usually has surge suppression built in, so why the need to add another one, right? Still, I'm curious if a better-designed surge protector like the Tripp-Lite one would trigger UPS failures. Possibly not.)
OTOH, a simple non-surge power strip with just a switch and outlet taps should surely be OK, shouldn't it? I mean, it's basically just a multi-tap extension cord with a switch... wires and plugs, and no other circuitry.