How do the apps that scan the NFC chip in a passport to ZK proof prevent fraud?

What type of fraud are you curious about?

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Allegedly a designer.

Input > ZK proof that I'm from the US based on a passport

Just fake the input?

What do you mean fake the input, though? You need to hold a passport. Are you asking "what if somebody else gets access to my private key"?

The proof comes from you signing a message with a key that is probably issued from the country.

Basically, all countries have a known public key and act as certificate authorities, kind of.

So, because math, I don’t think you can fake having one of those keys.

No, I'm saying what if proving you live in country X is valuable.

Wouldn't you have people creating fake NFC chips with seemingly real passport data from country X?