Chord DACs don't do real DSD native, they convert internally to PCM.
It would be trivially easy for me to do a native DSD DAC conversion using pulse array - so why don't I? It's because DSD to analogue conversion is horribly sensitive to clock jitter, and requires complex analogue filtering to remove the huge amount of noise above 20 kHz - and to do it efficiently enough so that noise floor modulation is not an issue in amps down chain would require hugely complex analogue filters - all adding distortion and noise, and more importantly the extra analogue complexity would degrade transparency.
The sensitivity to clock jitter is down to the fact that DSD is switching dependent - that is the effective switching rate changes with signal level. This induces signal dependent glitch noise, which creates large amounts of distortion. Moreover, this jitter errors also creates noise that is dependent upon the DSD modulator, so modulation noise gets decoded and inter-modulated into the audio bandwidth - this creates the well known idle pattern noise (a kind of gurgle sound, particularly noticeable when the music signal stops, and the DSD modulator recovers to zero idle patterns).
So if you want more distortion and noise, gurgle sounds, increased noise floor modulation and reduced transparency than go for the simple native DSD DAC.
I think this is not true, where did you read it? The manual states in a very clear way:
native DSD via ASIO.
Anyway, I would like to warn once again: the software players digital volume control does not work in DSD mode and the signal is output to its maximum. If somebody listens to some wav file through the Foobar, using direct output to the earphones, and downloads a DSD file and decides curiously to check how it plays, when switching over in the Foobar to DSD output mode and if having the earphones on, one might blow up his own ear-drums, no joke about it. I have had similar experience once, luckily with floorstanders, I nearly blew out the windows...
The confusion here is that there are two types of native DSD. There is the conversion to analogue, where you take the DSD bit-stream and essentially low pass filter it - so called native DSD conversion - with all the SQ and measurement problems this entails as I discussed above.
The second meaning of native DSD concerns not the method to convert to analogue, but the method to get the data to the DAC - the interface protocol. We have two options - DoP transmission, or native transmission. With DoP you transmit it via regular PCM, with a 8 bit header that tells the DAC that the bottom 16 bits is regular DSD data. With native DSD transmission, the data has no overhead, and is just DSD data transmitted, so the DAC receives a bit clock, DSD data left and DSD data right. Native DSD is more efficient, and you can run up-to DSD 512 - but the downside is that it is only via ASIO. DoP has the header data, so is less efficient, so will work only to DSD 256. The DAC than has to decode the DoP file to extract the DSD data - in an FPGA this decoding is trivial to do.
Both DoP and native DSD ASIO transmission protocols transmits identical data, and the DAC will receive identical data irrespective of whether it is DoP or native transmission.