Nope, I think you guys have got the wrong end of the stick here somewhere. In twenty years of training I have never been taught it as being across, ie as moving on a horizontal plane, always diagonal type technique. If you think about it, you would have to have the elbow pretty low throughout in order to accomplish this.
Also, I don't believe in teaching it differently to beginners, it's pretty simple whichever way you do it. The difficulty lies in the co-ordination of hips and arm, and I can't see how the elbow position at the beginning of the technique can influence this.