I've used Deb Tuckers Corner Pop ruler which I think is a similar idea to the folded corners ruler. With Deb's ruler you cut the base as a square and then trim off the corner with the ruler. This trimmed corner is then waste. But then what you sew onto that trimmed corner is a triangle. This triangle replaces the square with a line drawn in it. I think that's where the 'saving fabric comes in'. The second triangle is cut as a triangle, so you don't have the trimmings from that.
Hope that makes sense!