To the Vandy backers, the speakers' time and phase correct design makes the sound more natural and accurate, and that this type of design will make for a smoother sound than other speakers with similar frequency responses, because the time domain errors on other speakers create a more smeared sound that subjectively makes the speakers sound brighter even if they measure almost identically in their frequency response. This is akin to how a speaker sounds brighter in an echoey room where the reflected sound creates more audible time domain problems.
Careful. No one, too my knowledge, non one has demonstrated in controlled audiblity tests such claims of audibility on 'phase and time' correct, as a specific function of that trait as you are describing. ABX trials of such time/phase modified signals agasint controls, in a single dimension(headphones), of music and specific transient signals is very interesting, if you are interested in the actual effect on the sound.

Given a static room, the average room/on-axis balance is exclusively a byproduct of a speaker's polar amplitude response.

-Chris