I hadn't come across these shelters before, at least nothing so elaborate. Some of them could be a base camp for quite some time.
http://www.youtube.com/watch?v=gbcbGh2YsUkIt seems to me that the parachute cloth (untreated) stops drafts and reduces air movement but allows permeability for moisture management. In cold conditions, that's crucial.
I agree with your assessment:
In dry snow conditions, it would make sense for the parachute nylon to go over top of the reflective mylar (and plastic if you have it), hopefully creating extra dead air space for insulation and breathability.
If rain is likely, though, breathability would take second place to keeping the interior dry, so the plastic would go over top of everything.
The versions with open fires out front would require a lot of careful attention, given the relative flammability of the shelter materials.
I'm going to be knocking down some small trees and brush on my property. Maybe I need to build one of these for laughs.