The term "FAT" as he used it could go either way. Thickness, or width since it really isn't a technical term, sure some companys brag about fat bases in regards to the thickness, but lets not be retarded here. Fat can also mean wide. The base, as you yourself have described it has a thickness and a width.
However my complaint with your nit picking was two fold,
The waist is the center width, the dimensions of the ski were increased at shovel, waist, and tail. Not only the waist.
Obviously a thicker base isn't gona give you more than the mm's of float the new thickness is, so by fat we can safely assume he must have have been describing the base's overall width, not only the waist width like you called him out.
if you're gona nitpick...