First, not an 'arguement' but a position based on analysis.Yes, the argument was that the two graphs can not be the result of noise affecting the measurement of identical things. It would be impossible (or at least highly improbable) for randomness to conspire to plot these two curves based on measurments of identical test subjects. The difference cannot be explained away as noise. Since we don’t know anything about the test setup we simply have no idea what caused the difference.
Both plots are noise. Noise is random.
If run on the same device in a convoluted manner with ERROR/UNCERTAINTY added at each step and dealing with 30 uV levels no conclusion can be drawn. Only that inferring the null difference signal 'noise' or residual is due to the power cord is absurd.
The noise does not come from the power line. There are no 10,000 Hz harmonics in the power line and RFI is xxx kHz and xx MHz range.
The 50 Hz is not noise, it is interference.
Noise sources typically can't be identified.
The compared a 0.2 sq mm vs a 0.5 and their product is better. Why not compare a 0.5 to a 0.5 from 0 to 450 Hz? 9th harmonic. We know why.