I have a fairly expensive line-interactive unit that can be tricked into doing bad things just by power cycling my laser printer which is plugged into the same circuit (but not the actual UPS). One day this caused me more trouble than it was worth WRT lost work. I would have been better off plugged directly into the grid and just taking the 100 millisecond voltage dip at the PC's power supply. This is one area where buying high quality PSU can go a long way. High wattage Seasonic units can ride through some pretty nasty conditions before needing any outside help.
I also have a cheaper passive-standby modified-sinewave unit which has never misbehaved in terms of trigger conditions, but it is hot, noisy and otherwise does not inspire any confidence when it's running on its inverter. I would also never dream of plugging anything into this unit that uses a non-switching power supply.
Again, I am faced with the reality that you get precisely what you pay for. I always assumed double conversion was expensive paranoia never for home use, but over time this has proven out just like everything else when looking at the value equation of technology.