Of course Government agencies or the cops with a court order could get them.
What you are saying is true for certified copies, with a raised seal.
You can get usually get non certified copies even if you are not the person on the document or related to same—the non certified copy has no legal import, it is just a copy of a public record.
Each state has its own rules, but unless you are requesting a copy with a raised seal, it is a public record.
I don’t see how the government can claim otherwise.
The same holds for death certificates in some states. If one is not the spouse of child of someone who is deceased then getting hold of s death certificate is not always allowed. Those who work at all in genealogy can attest to that.