On the aeroplane I fly (Embraer 145), the line for minimum zero fuel weight is the bottom of the C of G envelope and is co-incident with the line for lowest aircraft weight.
I reckon that there isn't techincally a minimum zero fuel weight for the aeroplane, merely a minimum FLIGHT weight. I imagine this is something that was defined during testing when determining Va and generating that graph that you see which plots g loading against speed for a given gust if you know the one I mean???
Not sure if this is a load of old pants though, but I did some research into this too a while ago and couldn't get anywhere.