Darkbreeze :
They're talking about being plugged into the output of the UPS, they're not talking about the UPS being plugged into the surge protector.
Using Schneider Electric's reasoning, then also do not plug an extension cord into the UPS. Since that does something similar. Using Schneider's reasoning, an extension cord can also compromise UPS operation and voltage to the appliance.
Using Schneider's reasoning, a power strip that might reduce UPS output voltage will also reduce UPS input voltage. Causing a UPS to switch to battery more often and shortening UPS battery life expectancy.
If safety ground can be compromised as claimed, then an extension cord also creates that problem. Their reasons come without numbers. Subjective reasoning can claim almost anything regardless of reality. Add nunmbers and those fears evaporate.
Reality is this. A UPS in battery backup mode can be some of the 'dirtiest' power. For example, this 120 volt sine wave UPS outputs 200 volt square waves with a spike of up to 270 volts. That can degrade or harm a surge protector. Protector's response to that 'dirty' power may also confuse or had even even damaged some UPSes.
A UPS output (200 volt square waves with a 270 volt spike) is also ideal power for electronics. Because protection inside electronics is often equal or superior to what a power strip might do. Best protection at the appoliance is already inside the appliance to make surges and 'dirty' UPS power irrelevant.
OP defines a high quality protector only because it is $80. Most $80 strip protectors are electrically equivalent ot one selling in WalMart for $10. If high quality, then manufacturer's specification numbers (not price) define it as high quality. Monster has a long history of identifying scams. Then selling an equivalent product with expensive looking paint for even higher price. A Monster $120 power strip was electrically equivalent to one selling in Walmart for $10. Monster has a long history of doing this. Same also applies to some devices relabeled as power conditioners. It only is as good as its specification numbers. Price says almost nothing useful.
A protector that somehow filters and absorbs a surge may be a thousand of joules. A surge that tiny is often converted by electronics into low voltage DC to power its semiconductors. Electronics that use 'dirty' UPS power also convert hundreds of joule surges into useful electricity. So what does an $80 power strip do?
OP's concern should focus on another surge that can actually overwhelm existing protection. That surge is only addressed by a completely different device, unfortunately, also called a surge protector. Since even a UPS and $80 power strip also need protection afforded by the other (and less expensive) solution.