There are probably two clock domains--the 0404's own, and the PC one, and an ASRC converting from one to the other. Indeed, this is what Benchmark does as well.
The problems of ASRC are discussed on Bruno Putzeys section in the prosoundweb forums (he used to be chief engineer at Philips Digital Systems Labs for class D audio so he knows his digital).
The alternatives to ASRC are:
- deriving the clock from the incoming stream with a PLL and filtering the jitter down, which is what most regular DACs do, and is the worst solution with the exception of a few DACs I've read about that used fancy dual PLLs to get very good cleanup of jitter in the audio band
- as above, but using a high quality digital PLL that can completely filter out jitter in the audio band; this is what the brand new ESS Sabre DAC chip does
- send the DAC clock back to the source over another cable, or scrap S/PDIF and use a custom interface that accomplishes the same, and so then the incoming stream only needs to be reclocked and maybe slightly buffered; this is what a few high end DAC/transport pairs do, and a number of DIY designs
- use a VCXO (adjustable clock) and a buffer and slowly (at rate below audio frequency) speed up or slow down the clock to keep the buffer from under- or over-flowing; this is what some Lavry DACs do (and others don't even though they were supposed to

)
- a variation of the above with a fixed DAC clock hopefully close enough to the jittery source clock and a very deep buffer that is emptied or refilled depending on whether it's close to under- or over-flow during moments of silence in the music (such as between tracks); I have only seen one design (a DIY one) that implements this, and maybe some MSB DACs do but I can't remember and I'm too lazy to look it up, and this option suffers from latency and is unusable in cases where you need to have audio synchronized with say video, as the timing could become as much as seconds off
- use an asynchronous interface, which is what these new Wavelength DACs do (and I as well, though the rest of my DAC isn't ready yet)--this is purely a digital interface with no analog timing data transmitted, and is the proper solution that should have been standardized from the beginning, instead of the misery of S/PDIF necessitating various complex and non-standard workarounds