This conversation grabbed me, and I found myself thinking it about it while I was riding today. In this case, isn't everyone right to a degree? It seems like, by removing stem spacers and installing a high rise bar, Andrew was both increasing reach AND increasing effective stem length (or, at least the horizontal distance between grips and steering axis).
From what I can see, if you add or remove stem spacers without changing the bar or stem, then you are modifying the effective reach and stack. That is, if you remove stem spacers, the horizontal distance between grips and bottom bracket will increase (and the vertical decrease) but the relationship between the grips and the steering axis will remain the same. So the increase in horizontal distance is in the reach.
Similarly, if you add higher rise bars to a bike, but keep all other variables the same, you are increasing the effective stem length by moving the grips further away, horizontally, from the steering axis.
Every time I start thinking about this stuff I realize how incredibly complex bike geometry really is! There's just so many variables here I'm not taking into account (and not at all equipped to) I'm not sure that I really know anything about how to make a bike ride well.