Oh the earth neutral issue gets complicated. Transformer eddy currents can screw up the most carefully laid assumptions. The reasons why neutral is and never could be earth is the stuff you stamp your feet on is a different universe than a center tap in a wye or delta wound transformer. That center tap is called neutral and it's a hell of a long way from there to earth ground. Bonding between transformer center tap and earth ground takes place at the home or facility: Service Drop.
Do NOT mess with a very complex engineering plan for safety -unless- earth ground is not available at the receptacle. Connection to a receptacle minus an adequate correct ground is playing Russian Roulette.
Well-meaning campers down here have rigged BOOTSTRAP GROUND wires where a stub wire connects neutral to the ground pin DANGER WILL ROBINSON! It pays to understand why the National Electric Code DEMANDS electrical circuits be routed and connected a certain way with no shortcuts. It is to save lives and minimize property damage.