Is that proof going to require documentary evidence that both parents were American citizens at the time of birth???
That understanding, that you're presenting here, is disputed among conservatives and others, as to whether that is a requirement. You may think so, but others think not.
As far as I can see, this kind of requirement that is spoken about here on Free Republic with a few Freepers maintaining that this is so -- is only going to be resolved by a Supreme Court decision.
You're not going to find any legislature that will pass that kind of specific requirement into law -- but -- you will find that state legislatures will have a relatively easy time of passing a law that requires a birth certificate to be shown or else the candidate cannot be on the ballot.
Then all of those legislatures will just be engaging in a waste of time.