That's not my experience. Modern power supplies in desktop PCs either don't work or trip up non Pure Sine wave UPSs. I don't know the technical specifics but it has to do with Active PFC on power supplies.
I've used square wave UPSs on my PCs for as long as I can remember with power supplies from varying manufacturers, I have never had a problem. I have heard this before but I suspect it's either a myth or it only was ever a problem with very rare combinations of poorly-made UPSs and poorly-made power supplies.
I was forced to change UPS relatively recently (a few years ago) because the cheap but not bargain-basement PSU on my computer didn't work with the non-sine-wave output of my UPS. Call them poorly-made if you like, but either I got unlucky or they're fairly common.
Power supplies tend not to advertise their compatibility with non-sinewave power, but UPSes will certainly make it clear if they produce sinewave output. So the safe option is to get the UPS which gives the PSU what it's expecting.
