How are you convinced of this?
It seems counter to the vast number of modified sine wave UPS out there, that quietly do their job. If it's true that these modified sine wave UPS's have been killing components, wouldn't it have been discovered by now?
A properly designed switch-mode power supply will indeed handle modified sinewave or squarewave input with no problem.
First thing a power supply does when it takes in power is to rectify it to DC and charge a capacitor before feeding it to the rest of the circuit.
Many are also rated to run on straight DC. (Example: A supply specsheet I have here says: "90-264VAC, 127-370VDC input.")
Cheap ones might have an issue with the rapid turn-on of squarewave AC as opposed to the gentle slope of a regular sine wave. They can skimp on things like the input capacitors, diodes, or just about anything in the unit.
Two power supplies: Cheap generic junk on the left, and an Antec Truepower on the right.
Cheap junk has two 330uF caps. Antec has 820uF. There's also more heatsinking, dedicated filter and a beefy rectifier on the input, chokes on the output, and more filtration and regulation circuitry all around. All that helps to reduce the noise that ends up on the output lines, and the big caps work to filter out glitches in the incoming power feed.
If the OP's power supply has undersized input capacitors, then the switchover time of the UPS might be longer than it can handle. That results in a power glitch on the DC side, and the motherboard complains about it.