Granted my own background is different but my late teacher was in Tohei Sensei's lineage pre-split and for a while after; she trained with him quite a bit in Calif and Hawaii and her own teaching was based on that. I never heard her reference "koshi" in discussing four principles, power or movement.
That's perfectly understandable to me Janet. The west was interested in hara and not Koshi.
As I said it was of no significance to the Japanese for they were brought up knowing it. What someone like Tohei would see and note is the emphasis those from the west put on upper body and force thus the principles are to let go of all that and learn centre and relaxation.
One point leads to the stillness of mind.
Relaxing, weight underside leads to the understanding of Koshi.
Extending Ki leads to the understanding and use of Hara or centre.
I must say that I too never heard Tohei emphasize Koshi as such but did explain such things as dropping centre. When you see him do such things and watch carefully you will see it's not from the front so to speak but from Koshi. The west tend to put all this down to a low centre of gravity and look no further.