EDIT: That "always" is assuming the house is modern wiring and not older-style two-prong wiring for the wall outlets. Those systems were just main and neutral at the box and controlled by a fusible link.
If I'm understanding you correctly, in the US the ground wire is functionally identical to the neutral due to the bonding. Therefore (this is my own deduction and I'd appreciate being corrected if I'm wrong) you could, in theory, invert the ground and neutral wires in the plug of an electrical appliance and there would be no change in the behaviour or safety of the appliance?
Generally, no. I've seen backwards wiring jobs cause 48-80VAC to run through the casing of microwaves (they usually use the casing as a floating ground.) Any wiring inversion will usually cause some issue somewhere.
http://ecmweb.com/code-basics/grounding-and-bonding-part-2-3
Forgive my ignorance, I'm no electrical expert, but did you just say that the ground wire is connected to the neutral somewhere in the circuit? Or did I misunderstand you?