Sorry if this has been said.. it's a long thread!
Those linear power supplies (which prefer to draw their line current in big horrible spikes, and would love a chance to intermodulate your music with rectified line voltage), combined with the inherent nonlinearities in both class AB and D output stages, tend to complicate amplifier design a bit more than Andrew is letting on.
Using huge capacitor banks, minimizing dead time (in class D), raising bias current (in AB), shielding, etc. all reduce the distortion and noise somewhat, but what really makes the difference is the control loop.
What makes the Axiom amps better than the previous generation of class D (and what I'm surprised I haven't heard people talking about) is the way they generate their switching signals; they are essentially self-oscillating delta sigma modulators (similar to a lot of ADCs / DACs). The control loop in this type of amp acts as a low-pass filter for any signal that shows up at the input, but a high-pass filter for the noise that's generated inside the amp. This essentially separates the "good" and "bad" signals into different frequency ranges, with the "bad" being moved up where you can't hear it, and then directed right into the stop-band of the output filter. It also lends itself to tight control with high loop gain over the whole audio spectrum, and allows the control loop to accurately account for the time the output stage spends in between the rails.
I could see it being sensitive to higher frequency EMI though.. hence the linear supply?