I have a feeling that we're often misinterpretating the various planes involved because we wrongly assume that the plane line equals the target line. "Turning left" can simply mean striking the ball a good while before low point, when the club is moving down, forward and out. And it takes an open plane line to produce a divot that goes down the target line.
When I do air swings in front of the mirror with a wedge, I swing from TSP to TSP if I aim to the right of the mirror. If I aim straight at the mirror I look steep & high in the back swing and really flatt in the follow thru. And the hands start turning left before the ball is struck. I am pretty sure that I do the same on most strokes when I play too. But perhaps not with the driver.