What is interesting here, to stretch the visual analogy, is that something could be colored and STILL have a high degree of transparency. You would only lose transparency in the event that something you are looking at was MASKED by the color of the glass you are looking through. I have heard situations where the overall presentation was highly transparent and all images, space etc. were well resolved but there was a pervasive coloration to the tonality. If that tonality is caused by simple linear distortion (i.e. frequency response errors) then it may not have any impact on transparency whatsover (like the AudioStatic ES100s or STAX ELS F-81s, which were über transparent...but tonal balance was not neutral) but if it is from cabinet resonance, driver break up etc. then there is a situation where the distortion is masking the intended frequencies and this may impact the ability to hear "into" the music. Noise-floor of a speaker will also impact this "hear into" quality greatly.
For electronics, it has a lot to do with noise floor and signal CORREALTED noise floor. If the noise floor is being impacted by distortion components that cause the rise and fall with level, this will negatively impact transparency.
Interesting. Can you list even one type of system-related distortion that does not impact the noise floor?
And if as you say the noise floor negatively impacts transparency, isn't every other aspect of the presentation likewise negatively impacted?