i think they tell you to only cut the square's triangle because leaving the rectangle's corner intact will add some stability...but it also adds bulk.
i use a different way totally to make flying geese blocks, it works great for me and you make 4 geese quite quickly
for a 6 1/2" flying geese unit...
cut a 7 1/4" background square (this is going to be the center triangle part)
cut (4) 3 1/2" squares. draw a line diagnally from corner to corner on each of these squares.
line up one square on the corner of the background square with your drawn line pointing from the corner to the center. line up a second square the same way on the opposite corner, so the 2 squares overlap a little bit in the center and the lines are lined up even. place a couple pins to hold them in place. stitch 1/4" on each side of the drawn line. press flat to set the seams then cut on the drawn line. take to ironing board and lay it down with the large triangle facing up, press and fold it back so the 2 (points) underneith are showing, press. (the seam will be toward the large half.) take your 2 left over squares and place them one each on one of the units you made lining up the corner with the drawn line running from corner to center. stitch 1/4" on each side of the line. cut apart and press as before...and you have 4 flying geese units complete.
i do use the elenor burns flying geese ruler to square up my blocks but these turn out so good, and easy...i used to hate making flying geese units, now they are a piece of cake :)