Riiight. You guys are seriously claiming that there are people who can hear the difference between class A, Class C, etc?

That is a DBT I would love to see!
You will hear a difference between amps. However it depends on what the amp is driving.
The problem is that speakers are not resistive loads. They are inductive and in some cases capacitive loads. In an inductive circuit voltage leads current by 90 degrees. In a capacitative circuit current leads voltage by 90 degrees. This among other ills, as all at the heart of the problem analog passive crossovers.
Now the speaker designer says to the amplifier designer, make your amp sound as good with any load my speakers produce at any audio frequency.
The speaker designer says to to the speaker designer, your loads are a torture test, and if I have to do a good job covering that eventuality it will be expensive.
We have already had the Dynaudio example above. Now I don't know the current Dynaudio crossover circuits, but that used to publish them and liked a minimalist approach.
Now these speakers use a couple of Dynaudio W17-75 EX with D 28 AF tweeter. The crossover is mine.
http://mdcarter.smugmug.com/gallery/2465549#129315000
Now the impedance drops to almost three ohms, and the phase angle changes from +90 to -90 degrees over the operating range of the bass mids.
Now most amps will just not do a decent job of powering those speakers. However my current dumping amps do. I have run into numerous situations were changing amps can be quite dramatic.
Now the other issue is that the industry tends to be geared to a price range. For speakers at the lower price breaks, I'm sure the designers try and avoid over complex loads, and sacrifice items like total diffraction compensation in many instances.
The other issue is crossover distortion in amps. Now this can be hidden by manufacturers in their spec sheets, as it is an atypical form of distortion. This is the hall mark of the ubiquitous class AB amps. You can see it on the scope best. I personally have become highly sensitized to even small amounts of crossover distortion and I hate it. It is hard to describe audio aberrations in words. However the word that comes to mind is gritty. Amps that don't have it sound much more relaxed, and provide me at least with a fatigue free listening experience.
And it goes without saying that the more accurate the speaker system the more these type of issues are discernible.