(Replying to your comment but most words here are written for others to read – I know you know all this, and you may well have corrections or clarifications to add 
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100% this. There’s a fascinating conversation to be had around this and very few people seem to be willing to have it. I only had my eyes opened when the first descriptions of how the DS DAC performs upsampling came out and it nearly broke my head.
All digital audio plots amplitude versus time. Not just PCM, but DSD and every other variant of PDM as well. Any audio transformation you can perform on PCM you can perform on the others, and if you provide sufficient precision you can do it losslessly, or near enough to not matter. DSD purists think that anything with more than a single bit per sample must by definition be inferior – but in the same way that jitter only matters at the point of A/D/A conversion, likewise the 1-bit-ness of DSD is only an advantage for physics reasons related to the construction of audio electronics.
As you point out, Ted, in the pure information domain the key is the super high sample rate, and I would add to that the noise shaping which mitigates the 6dB SNR of direct 1-bit sampling. Compact Disc and its “PCM” brethren use lots of bits to provide high SNR across the entire sampled frequency spectrum, which is a narrow but deep approach. DSD uses a single bit but at least 64x the sample rate of CD – wide but shallow – with sigma delta modulation to provide a high SNR in the audible range and pure noise in the upper frequencies.
But they are fundamentally both plots of a waveform. Waveforms can be scaled, added/subtracted and transformed in a myriad of other ways regardless of how many bits per sample they have. You do need to have more bits in your answers than what you started with to avoid losing your signal in quantisation noise, but whatever it is that allows DSD to sound so good is not lost in this process, especially if you’re merely adjusting levels and mixing multiple tracks together.
And why does DSD seem to be able to capture and hold better sound than low-rate PCM? I don’t think you mentioned it in this thread but you’ve made the point elsewhere: it’s the filters. Because the Nyquist cut-off (half the sampling frequency) is so far above the audible band we can use far gentler filters which avoid roll-off and group delay in the audible band; filters which are needed during recording, in the digital realm prior to SDM processing back to 1-bit, and in playback equipment to let the audio out without all the ultrasonic noise.
DXD is both wide and deep (32-bits). You can bring your DSD recordings into that space, transform them without losing any of the benefit of those shallow filters, mix them directly with PCM content if you need to, and then run an SDM process over the whole lot (which includes another low-pass filter to eliminate the ultrasonic component of the DSD waveforms you mixed in) to produce a final DSD output.
(Edit: the paragraph above is wrong because I forgot that DXD downsamples to 384kHz. So it’s good but not as good as what Ted does at full sample rate inside the DS DAC.)
DSD doesn’t lose its essential quality as a result of being processed through what is indistinguishable from a PCM system, so long as the high sample rate is maintained the whole way through.
