So I’ve never done it, but if I wanted to run for office, I would have to file for it with the Secretary of State, and presumably present proof that I am eligible. Didn’t Obama already have to present similar proof to 50 different Secretaries of State to get on the ballot in each state?
In a word. No. You presume too much. Apparently NO ONE is tasked under the law to ask for such documentation from would be "public
servants masters". In some states, apparently the parties are supposed vet their candidates, but no government authority checks up on them.