Here's my take on it. I think the power-supply design is legit, but the marketing is kind of a gimmick. Their explanation of more instantaneous current being available is a legitimate. An inductive load (like transformer windings) will resist changes in alternating current through the load. Using a higher alternating frequency (like in a switching supply) allows using smaller inductors to smooth out the output, thus presenting lower impedance through the power supply. In Burson's case, I *think* they're using an off the shelf switching regulator with a switching frequency of about 170 Khz, which should be well above the audible range. Being that these are off the shelf solutions, acting as if it's a revolutionary new design is a little disingenuous from a marketing perspective, IMO. That's where the "gimmick" is to me. On the other had, I understand why they feel inclined to do so, since the audio community tends to have an automatic bias against switching power supplies, however well designed. From my experience so far, I think they made the right decision with the power supply from an engineering standpoint.
If you were to add your own linear power supply, it would likely be detrimental, and it's unclear whether doing so may damage the unit, as it has with some recent Monoprice/Cavalli designs with similar implementations. With an external linear/regulated supply, you'd lose the low impedance benefits, while the internal switching regulators would still convert the input to a high-frequency AC waveform regardless. I can see no benefit being gained from doing so.
To be honest, I'm starting to be convinced that with a well designed switching supply, there's almost no case where a linear supply would be a better design choice; you would have to spend so much more in parts cost and space (as a designer), to achieve equal or better results as the well-designed switching supply. You have to remember that Burson used to be one of most ardent advocates of big, discrete, linear power supplies. The fact that they're changing their mind says something. Even the upcoming dedicated power supply for the Headamp Gilmore Lite Mk.2 is a hybrid-switching design. These aren't "your grandfather's" switching supplies haha.