Legal claims at birth via citizenship by descent are all that matters as far as a father is concerned. Under the law, a bastard child given birth by a married mother is the legal issue of her husband.
That is the case to this very day. How many cases of men being forced to maintain child support for the biological offspring of another man have we heard about in just the past several years?
Quite a few.
But, those local statutes cannot be used to control the meaning of terms in the Constitution. If some of the Founding Fathers thought that the citizenship of a child's parents was important to NBC status, they meant the real parents. How local governments handled child custody and support issues would have been of no significance in creating Constitutional qualifications for Presidents of the United States.