Handwaving is not engineering.
Nor is your display of limited knowledge of the real things that might affect measurements so they are not what we expect them to be.
Gawd help us when we don't see the result on an oscilloscope that we expect !
What might cause it when all known things we can control are excluded from impacting this measurement ?
Simple deduction in this case of distorted mains, we wrongly consider mains as a infinitely low impedance current source and while it is quite low it is NOT the perfect current source that we might base calculations on therefore it's
presumed perfect sinewave is influenced by every mains grid users current loading to be what we measure and see.
As is the case with a low impedance current source, use of voltage measurement techniques like 10M input DMM's and 10X (gawd forbid
) probes has an infinitesimal influence on such a low impedance current source so for any practical purposes we can disregard them.
Distorted mains is a fact of life, get over it and get on with life.