Ah, the wording; gender or sex? improper wording in documents? Can't tell the gender at birth, and in some cases even the apparent sex isn't accurate or meaningful, just looking can still be wrong, and even genetically it isn't just binary. There's the genetics (medical, historical), physiology (id, medical) and experience (id, gender), three things actually, matching or not. To be accurate you'd need at least three boxes to choose from in the birth certificate, and at older age add another three or four, amending the "sex" indicator as appropriate, or leave it out entirely in some documents when not needed.
I'm with MM on this, changing birth id is rewriting history to feel better. I think it should be kept at least for statistical or historical research and possibly medical use, but needn't be divulged without proper reason with special consideration for TS persons. How Angela told us it was sounds pretty good to me, don't falsify originals but provide cover. I assume and hope getting a new copy wasn't made difficult intentionally.