1. But, a passport is always proof of citizenship, right?

No, actually it's not.

In many countries, you can have a passport issued to non-citizens (See Jordanian temp passports for Palestinians, refugee travel documents i.e. "Geneva passport, Armenian special passport, etc.).

Fun fact: even a U.S. passport doesn't necessarily demonstrate the holder is a U.S. citizen (they may be a U.S. non-citizen national).

In my experience, most American citizens don't even know there is such a thing as a U.S. non-citizen national.

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