Where do you live, that anyone with the requisite fee can get a copy of anyone’s BC?
State laws differ.
When I lived in Iowa, birth certificates were filed in the county courthouse in a record book that I checked weekly for new births. The newspaper I worked at wanted to print the names of all babies born in the county every week so we went and checked the birth certificates. Never had any problem. Just went into the vault, got out the book, and copied whatever I wanted from the birth certificates, marriage licenses, and divorce decrees.
Sometimes I got curious and when I had some extra time went into the really, really old records ... like the early 1800s. It was all there for anyone who wanted to look at it.
A birth certificate, marriage license, divorce decree, etc., is a public record unless sealed for reasons such as adoptions or custody disputes with juveniles.
If anyone tells you differently, ask them to show you statute law on the matter in your state.