Is the reason some headphones perform better in soundstage lays in presenting better layered similar frequencies with slight changes in phase better?

It may be due to EQing the headphone to mimic head related transfer function (HRTF). Normally when you hear something from the right with your left hear you get a set of changes to the sound corresponding to the shape of your face, head, etc, depending on them our brains get a better idea of where the sound source is.
 
Just as well it may be due to the headphone having low enough distortion that allows you to hear fine details about recording studio accoustics, feeling of space is usually already in the recording.
 
It may be due to the driver postioning and earcup accoustics that create some sound relfections that we hear as additional soundstage info.
 
I doubt it's a thing of phase, because I don't think that it's possible to control headphone's phase response to that extent, or maybe it's just lack of phase related distortion or some phase shifts caused by membrane resonances...

Phase is an issue with speaker soundstage, particularly multichannel. But it's doubtful it makes a real difference in headphones. It's more likely the angle of the drivers and their position relative to the ear canal.