If I go into an Italian consulate with all the paperwork indicating that chain --birth certificates, naturalization papers, marriage certificates, etc.--I can get an Italian passport. Understand, this isn't applying for Italian citizenship. This is proving that I'm already an Italian citizen.
So, here I am, the third generation born on US soil, but Italian law says I'm also an Italian citizen. Am I a natural born citizen?
If you were born in the country to Citizens parents, then yes, you are a natural born Citizen.
Not if you can be claimed by Italy or can claim Italian citizenship.