The leather was skived down for thickness and the snaps are actually stitched between two of the layers.
Yeah, I had to skive the leather around the holes on my first (trial) bag just to make the snaps work. But how do you stitch the snaps between layers of leather? All the snaps I've come across (from the original ones to the new commercially-available ones) have a 'lip' around the edge. I can't see how that would lay flush between layers of leather without cutting off the lip.

This is the reason why the way the MoD had them made works so well. The snaps are actually stitched into a "horseshoe" of leather, which is stitched to the inside top of the bag. The bag actually floats on the studs/snaps.
Well, I'll be darned. My MoD sporran was not built that way. As you can see below, the snaps were stitched directly to the front panel, with the stitching showing on the front. The way you describe makes a lot more sense, though! I wonder why mine wasn't made that way. I see no evidence of there ever having been a 'horseshoe' panel installed.