Your comments are logical from the perspective of a quality...

Your comments are logical from the perspective of a quality source, but are they when there is no certainty as to the make-up of the recorded signal?

If the recording is exclusively of the output of the speaker then one would expect a sinusoidal waveform ... but would not the imposition of background noise distort the wave?

My world is electrical., not acoustic, but I seem too spend a lot of time these days examining recordings of highly distorted voltage waves because of the harmonics produced by modern electrical equipment. The resulting waveform is an aggregation of all the outputs on the supply, so what started off as a relatively clean sine wave becomes more distorted as more "dirty" loads are added to it. Is it not the same with this situation? In my case, I need to see the impact of all the devices in the building to be able to solve the problems, but I would hate to have to try to isolate one device from my recordings.