And yes, the PRINCIPLE is: Citizenship by birth.
Those who are citizens by birth are eligible. Those who are born non-citizens, and are naturalized later, are NOT eligible.
It’s really not complicated.
Discern the difference between “citizen by birth” and “citizen at birth”.
We know with certainty that “citizen at birth” is by naturalization statute - read the law.
“Citizen by birth” requires no such statute.