As for the amplifier relevance, both in general as well as in those measurements from that AES paper, it all depends on the measurerment strategy and the desired entity. We either want to see the effect of the amp or the cable alone, or both in combination, it all depends....
In my proposed setup, only the cable influence is measured, the amp's contribution is normalized out. The amount cable influence of course depends on the amp output impedance, amp impedance should be significantly lower than the cable impedance to see maximum effect from the cable. As explained, with a current drive amp, no change of speaker voltage (and SPL FR output) will form regardless of any series impedance... which is technically correct as per goal we want to measure the effect of the cable alone, and with current drive there is no effect by definition... obviously, the FR will be all over the place, completely spoiled (but could be EQ'd to flat), yet the cable itself makes no difference.
@pma's setup is slightly different. He also uses a ratio, though a different one: speaker-side voltage normalized to amp-side voltage. For very low amp output impedance it yields the same results, but for higher impedances the result start shifting away from representing the true speaker terminal voltage change. Again, using current drive as the exteme case for illustration, the voltage on the speaker will not change no matter what cable but the measured ratio is changing as it is measuring (V_speaker)/(V_speaker + V_cable)=1/(1+V_cable/V_Speaker). Of couse Pavel is aware of that and pointed out the influence of the amp impedance.
In the Davis Experiment, they used the same strategy, normalizing to the amp output, albeit they did it point-wise by manually forcing the amp output to be 1V at any of the test frequencies. Therefore, the effect characteristics seen are the same. Change of the (unknown) amp output impedances is reflected in the results even with one and the same cable, as it should be. And vice-versa, change only cables with same amp and get similar but topologically different results: the leg in the voltage divider where the variable is introduced now is the other leg, the bottom leg. Finally you can alter both legs at once and get yet another set of plots, less meaningful ones (two variables at at time -- no no).