Local birth certificates are apparently fine if they were issued by a local government authority.

https://travel.state.gov/content/travel/en/passports/require...

One of the "primary" forms of citizenship evidence is:

  U.S. birth certificate that meets the following requirements:

    Issued by the city, county, or state of birth
    Lists applicant’s full name, date of birth, and place of birth
    Lists parent(s)’ full names
    Has the signature of the city, county, or state registrar
    Has the date filed with registrar's office (must be within one year of birth)
    Has the seal of issuing authority

(Edit: I assume that if the State Department doesn't know how to validate a particular local government's birth certificates, it's supposed to contact the issuing authority to ask.)

OT: I followed the link to the rules given in the article. While there I ended up on the page that gives rules for passport photos, since I need to get around to getting one to renew my passport.

One of the rules (added in late 2016) is that you cannot wear glasses in the photo. However, if "[...] you cannot remove your glasses for medical reasons, please include a signed note from your doctor with application".

I've never heard of nor can can hypothesize a medical condition that would not let you remove your glasses while sitting or standing still for a photo. Anyone have some examples?