My birth certificate ( and that of my daughter) shows very distinctly what nationality ( ie where born) my parents (and her parents) were. Now I don’t know what info your state required but at least in Colorado and in California that infor is required.
My BC long form has (place of birth )for both parents,further delineated as (state or foreign country). Despite the document showing them to be born in the usa, that is not evidence of them being US citizens as it is self supplied. To be sure of that, their birth certificates or other information would be necessary IMO. See Sun Yat Sen hawaiian BC, its a lie.
ML/NJ
If you look closely at the Hawaiian long form BCs in post 4 above you will see that the birthplace of the parents is one of the required entries.