I wonder if it is more of the fact that:
"The two antiphase outputs are connected to the load in a way that causes the signal outputs to be added, but distortion components due to non-linearity in the output devices to be subtracted from each other". Isn't that the very definition of balanced?"
--Balanced Amp Wiki
It appears that the Balanced Ultra Desktop Amp is a type of push-pull ( analog case ).
One of the best ways to reduce noise is by using a differential amplifier.
I found a thread for anyone who wishes to read more about push-pull and balanced amplifiers.
In the end, if the BUDA is differential regardless of being in single ended vs balanced, I cannot fully explain why I hear less blurring in the bass and better soundstaging.
I will try to get someone from Headroom to comment on the topology of their BUDA. Perhaps when the single ended selector is active the amp is no longer truly differentiating??