> It was impossible for my wife to provide an up-to-date (less than six months old) translated copy of her Chinese birth certificate

I find this hilarious. It's the same in France, you need an up to date "original" of your birth certificate. But why? It's just saying you (full names) were born in XXX on a specific date. There's nothing about it that could change, really. In the country I'm from, your parents get one original on birth, and you can ask for copies from the town hall. But in France multiple administrations were extremely bothered that they weren't "original" (because they say DUPLICATA on them, and in French you get a shitty A4 with a stamped signature one can print at home, but they insist on an original) and weren't in French.