My Pennsylvania BC from 1956 only indicates that I'm legitimate under the "For health and medical use only" section. It was filled by the doctor. The section also includes info about syphilis, prenatal care, birth weight and stuff like that. There does not appear to be an affidavit connected to this.
Legitimacy is sort of a weird thing that I learned going back on an old family tree. (From 1827 - North Carolina) I won't discuss it because I did a few pages back and don't want to get off topic.
Legitimacy may have been in the health section
in my 1956 birth certificate to determine: "Would social services need to be contacted?"
When I worked in newborn in the 1990s, sometimes children of prostitutes got automatic social service referrals. Additionally, infants born to teens under 16, automatically received social service referrals.
Saw this site How to Go About Finding Your Illegitimate Ancestor's Father
Mexico had various degrees of legitimacy: hijo natural de, adulterino, (not married) espurio (fake father's name or unknown), bastardo, or ilegítimo.
Also different states based their laws on other locales. Texas has bits of Mexico in their laws. It's complicated!
Also noting Mexico, which was Spanish, which was Catholic and since Zarelli is Italian with recent immigration...maybe they had similar conventions in Italy?? Anyway, it's a gray area. I think investigators are very fortunate to have this information on Joseph's parentage.