A lot of the "don't use X with a UPS" (or a generator) thype items are really dependant upon the UPS/Generator. A LOT of them to NOT really produce clean sine waves, and produce a stepped wave that approximates a sine wave, and a lot of electronics does NOT like that (remember that a square step produces a LOT of harmonics (every Odd harmonic out to infinite for a pure square wave, but with each harmonic being at a reduced power, if I remember right 1/n with n being the harmonic)

Usually USP/Inverter/genny mfgs are worried about lightbulbs, fridges etc. The GOOD units worry more about clean signals

Back in the late 80s (I stopped working in electronics in 1992) the company I worked for made an AC power supply that COULD work off a battery bank - aka could be a UPS. It worked with everything from pure capacitive to pure inductive loads, and had a CLEAN sine wave, enough so that we had to use test gear usually meant for high end stereos to measure the number, and handled any amount of mismatch load wise on the phases (unless programmed to drop out). Of course Uncle Sugar was paying a LOT of money for them, but needed them for uses that didn't fit my 'need to know' (but the guys doing acceptance tests often showed up in undress whites)