Long story short--a UPS transitioning from line to battery makes most surge strips think it's a surge. They then cause (quite intentionally) a short. Bad for the UPS electronics. Do it often enough, and it's quite likely to cause a large enough short to blow both the surge strip and the UPS electronics.

A line-interactive and/or double-conversion UPS will take care of the spikes/surges. Only power bars (without surge protection) should be plugged into their load side.

Now, if you have a good UPS that puts out a true sine-wave (not an approximation, not pretty good, but an actual sine wave output), some of this does not apply. Unless you put the UPS on a bench and test it, make no assumptions that it's an actual sine-wave output.

Basically, square-wave output and stepped-wave output waveforms can make a surge strip think it's a surge/spike, and they short. That's bad for the UPS. Wikipedia sort of gets this right, but they don't really explain why (non sine-wave output waveforms are what cause the surge strip to go nuts and short).