Yup.
Modern Class D is pretty much at the same SQ level as AB. Many generations ago, class D had problems at the higher frequencies, it's just an inherent problem of the design that took a few generations to engineer out. But, damage was done, and Class D got a bad reputation due to the original problems.
Kind of like today when you get questions about "Plasma Burn In". Modern plasmas have pretty much engineered that problem out of existence.
Wiki gives you an idea of why high freqs can be problematic for class D:
A class-D amplifier or switching amplifier is an electronic amplifier in which the amplifying devices (transistors, usually MOSFETs) operate as electronic switches, instead of as linear gain devices as in other amplifiers. The signal to be amplified is a train of constant amplitude pulses, so the active devices switch rapidly back and forth between a fully conductive and nonconductive state.
If your devices can't switch on/off fast enough, the high freqs suffer. Modern class D, the disadvantage is that they don't have the headroom that you can get with class AB.
Now, as I mentioned, Class D and SMPS typically go hand-in-hand. My opinion is that SMPS has no place in Hi-Fi audio! There are many experts and several books that agree on this. The BEST PS for an amp is a simple unregulated linear supply. There are several reasons that SMPS are inferior for Hi-Fi applications.
BTW--The HK in question is Class AB. It is the Pio that is class D.