The reason why he gets a "granny" version is that he is starting off in the wrong way. When he crosses the laces in the first stage, he passes right over left and under. When he comes to the loop stage, he again passes right over left when making the loop from the front, giving the granny knot. If you start off with left over right, then the loops can be tied right over left, to give a reef knot, without the need for sending it round the back.

I always tie my shoes in the "reef knot" style. It was how I was taught as a child. If Mr Moore has been tying his shoes wrongly all his life then it is because he was taught badly in the first place.

DC