No proof required. Legally, the Husband of the marriage is ALWAYS the father. That *IS* a matter of English civil law which we kept.
Nevertheless, that rule is still the rule in many, many places. But, how can we force the U.S. government to adopt similar rules for purposes of its determinations of citizenship. I don't think they're required to follow state statutes and, even if they were, which state's statutes would prevail. Should NBC status depend upon what state the candidate was born in?
I think there are some holes in that analysis, parts we can't be sure were contemplated or intended back then. ;-)