1. just check this website: http://thume.ca/screentunes/ there is a large chance that your computer videocard and/or LCD will make a noise on that page
2. when the videocard makes such a noise, it can interfere with the PSU and thus affect the soundcard as well.
3. Thus, it's actually possible that changing a "high-frequency stripy" interface to a solid color will lower the noise-floor on the sound-card a bit.
The voltage across DAC-amp ground causes a DC offset seen by the amp (likely less than 1mV). The exact amount of voltage varies in time with CPU power consumption, producing AC that you hear.
You need to eliminate the ground connection between computer and DAC (toslink, USB optoisolator, etc.).
I think a difference just stimulates the brain, along the same lines of why supermarkets infuriatingly keep moving the products around so you can't just auto-pilot your shop.
I find that I have to shut my eyes or look away from the screen when toggling the modes to avoid biasing my perception of how the audio is changing. It's particularly bad because the visual changes are designed to evoke the effect it has on the sound.
In many contexts outside science, whether some sensory difference exists objectively or not may not be relevant at all as long as there is a perceivable difference in subjective experience.
"We made some test once, and we changed the skin of the software, to a new color. Every people said the software sounded better with that new skin. Yet we changed absolutely nothing except the color."
I'm still wondering if some graphical configuration ( such as a bright color) wouldn't stimulate the brain more, making it more receptive in general, and to sound in particular, letting people "hear" better.