Not sure I'm understanding your rebuttal - in your example are the doctors the politicians, or the providers of the voting system? If the two doctors are the politicians, then I think you are misunderstanding my point, and probably the objection raised that I was referring to. If your doctors are the people running the voting blockchain, then that's the whole purpose of having the chain - that it's mathematically verifiable by "anyone." This would be like if all the doctors in the world have a chance to oversee the operation and make sure it goes down smoothly.