That is a little backwords. The child is not claimed by any Nation rather the child by Birhright has claim to the Nation of his or her parents Citizenship.
Just like children born here of illegals from Mexico still have claim to their Mexican Citizenship.
An infant doesn’t actually “claim” anything, they are either claimed as a citizen under the laws of a nation or not, and usually issued such long before any act of individual volition.
So if England extends birthright citizenship to all Americans, nobody born with that foreign citizenship would be eligible for the Presidency?