We need to be careful that we are all using the same definitions and meaning of the terms used in the book.
For International style the IDTA use the term "straight" solely in relation to sway, where it is understood to mean 'no sway'. It has no bearing on the direction of movement or turn of body or feet.
I agree that we often see turn taken too early. The turn does commence on 1, mainly due to the use of CBM, but the step is still taken forward. Starting the turn too early results in the RF moving diagonally forward.