Wellllll the situation is actually more complicated than what people have been pointing out.
With DSD64, the noise will quickly rise after 20Khz. To combat this sudden jump in noise, designers will try to filter out all audio above 20K. This filter has to be exceedingly steep at 20K. In fact in a perfect world, the frequency response of your dac would look like a perfect flat line out to 20K, followed by an immediate drop to 0. This kind of filter is called a brick wall filter.
In a perfect world, with a perfect brick wall filter, you probably would not notice the difference between DSD64 and DSDXXXX.
Sadly, there is no such thing as a perfect brick wall filter. In fact most brick wall filters actually kinda suck.
What you will often times see is a filter that actually might start rolling off your audio at 18khz so that the filter can achieve a 20db roll off at 20Khz. Different manufacturers will do different things in order to tune this filter so that it does the least amount of damage, but it's pretty much a crap shoot. Of course that isn't to say that filters can't be done well, but it is exceedingly difficult.
With DSD128 and 256, the sudden jump in noise occurs muuuuch further out in the frequency response. This means that the filter can have a slower roll off and be placed well out of the audio band. Obviously, this means the filters are much easier to design well and are virtually inaudible.
Long story short, it's most likely the DAC's fault.