I am sorry that you cannot interpret measurements and determine how something is likely to sound @ricevs and/or if something will have no additional sound at all. Measurements can help you significantly with one, and completely with that other. That some audiophiles do not believe this does not make it true, it just makes those audiophiles wrong.
w.r.t. inverters, given every single piece of equipment will behave differently when exposed to a different harmonic / noise signature of an AC power source, the best that can be done is generalizations, and one of those is a well designed products will be immune to all but fairly bad AC power. Whether you accept that or not does not change that fact. Additional comments could be made, such as certain distortion characteristics could reduce AC hum on tube amps, or no/low global feedback amps may have issues with certain frequencies of distortion products. Beyond that, any comments made in careful listening tests, i.e. switching between clean AC, wall, and "inverter" which would have to be made in such a way to reduce listener error, would be applicable only to the specific equipment connected and except in the most egregious cases, which would be readily evident in measurements, would not be at all transportable to other equipment and other connections of equipment.
