The debate here is not 'have the windings reversed', but is the signal 180° out of phase with the active coil. I am thinking about this very carefully...Using your bolt analogy, if I take a threaded rod and flip it over, the threads still force me to turn the nut to the right. Those turns should reverse if I flipped the rod, but they don't because they are now turning in the opposite direction.
Sadly, I don't have suitable coils to experiment with, so I urge anyone that has to try this and report back with an absolute answer.