Yes, I don't find the examples very helpful either, but I also don't like ASR's general credo that amplifiers sound the same when they measure the same.
In my opinion, the measuring stations used are not complex enough or do not represent the truly complex load of a difficult-to-operate loudspeaker.
Even though modern amplifiers measure essentially identical at typical listening levels and into benign load, and therefore sound indistinguishable under those conditions, that does not mean they behave the same under all conditions.
Loudspeakers are not resistive loads; they are complex electro-mechanical systems with significant impedance variation, phase shifts, and back-EMF. Once the load stops being linear and the amplifier is no longer driving an idealised resistor, the operating conditions can shift far away from the assumptions of purely linear, voltage-source behaviour.
Depending on the design of the power supply, current-delivery limits, protection mechanisms, output stage stability, and the available feedback margin under stress, amplifiers can respond very differently when the load becomes demanding. This may show up as earlier or later onset of compression, different clipping behaviour, variations in how well the amplifier rejects back-EMF, or differences in stability when faced with capacitive or inductive components of the load. These behaviours are rarely captured by standard measurements into a fixed resistive dummy load but can become relevant with real music driving real loudspeakers, especially when high SPLs, low impedance dips, or extreme phase angles are involved.
In such situations, amplifiers, regardless of topology, do not remain indistinguishable. The practical differences arise not because amplifiers have a “sound” of their own, but because they differ in how far they can stay within their linear operating region under dynamic, stressful conditions. Where one amplifier may remain clean, another may already be limiting, invoking protection, or approaching clipping. And these behaviours can become audible, not as tonal coloration but as differences in headroom, dynamics, and control, which are at the end hearable.
In short: under normal conditions, a good amplifier is a good amplifier. But once a loudspeaker presents a challenging load or demands high, fast current peaks, the determining factor is not the circuit class but the overall robustness of the amplifier and his power supply. How well it maintains linearity under stress can vary and that variance is precisely where audible differences may arise, even though standard bench measurements into simple loads show almost no divergence.