"Let's keep this very simple. There is no turn in the first step of almost any figure"
There is not turn on the first step of MOST figures, but this thread was specifically about the fact that there IS turn on the first step of some, such as the weave following a whisk.
"first step is straight."
This is where it gets interesting. Even in the weave after a whisk, the direction of movement is relatively straight. What is turning at that point is only the alignment of the foot, not the direction of travel which will not change until later in the figure.
"My coach keeps it simple, if you are turning to (or commencing to turn to) any direction, take the whole frame with you."
That's the usual situation, but not all figures commence their turn by turning the body. In the case of the weave after the whisk, the fact that he is coming from promenade position means that the man's body is already well towards the alignment it will needs to have for the first step. But what does have to change by about 45 degrees is the alignment of his foot, and so that is what the technique book says turns 1/8 between the preceding step and step 1.
Body turn, foot turn, and change of direction are three fully distinct factors. Most commonly they occur sequentially one leading to the next in the order that I just named them, but sometimes as in the weave after a whisk, it works differently.