I just did a quick experiment and grabbed a razor and a hone off my desk.

It needs its bevel set any way so I am not hurting anything!

When I study my stroke the scales do shift slightly from the push to the pull stroke. Not a whole lot but from this quick peek I think that the pivot pin does does have a role to play in honing. These are relatively thin scales and not a thick handle so I think that the handle would have more influence.

Maybe this is how I learned and if I learned on a thick fixed handle I would have learned a different stroke?

Tim