I looked at the method you posted, and it is a completely non-traditional way of making a cathedral window quilt. That's why you need batting and a backing for it, to hide the piecing.
I'm not sure what the 4 square method is, but it sounds to me like the traditional way of making the blocks. Traditionally the blocks were made by hand, but there are ways to incorporate machine sewing in them too.
Here is a link to a tutorial on the QB that explains in detail a relatively fast, machine sewn way to make cathedral window:
http://www.quiltingboard.com/tutoria...al-t35742.html
Because of the folding, any of the traditional methods (whether done by hand or machine) will result in a finished back. All of the fabric folding creates layers of fabric in the quilt, so it is quite heavy even though there is no batting or backing.