The issue with computer power supplies (and power supplies in general) not handling the load has to do with 2 factors:
1. The sensitivity of the protection circuitry in the PSU. The more sensitive the PSU is to surpressing / shutting down voltage spikes, overcurrent, etc., the more likely the PSU will not run on modified sine wave power.
2. The load. Running on a modified sine wave power source is roughly 30% less efficient than running on a pure sine wave. This efficiency is taken off of the peak power handling of the PSU and rapidly increases heat generation. For instance, a 90% efficient 500 watt power supply (50 watts waste heat), on a modified sine wave power source, will only produce 400 watts of power but put out 150 watts of heat.
This is because of the duration of no voltage or less-idea-voltage experience due to the "steps" in the voltage levels. Some computer power supplies handle this well. Issues become more serious when used in electronics because their power supplies usually do not have the lee-way that computer power supplies have. A plasma TV with a 600 watt power supply experiencing a 30% increase in inefficiency and waste heat may not have the headroom to spare (180 watts of waste heat and power usage) when put on a modified sine wave UPS. While some TV's just won't start or will turn off when stressed too much, other's will simply burn out.
Kitchen appliances also tend to have issues with modified sine waves as control boards for clocks on appliances often rely on the sine wave to keep time. Microwaves will often burn out on modified sine wave power sources due to the 30% increase in power usage as will refrigerators.