> In the USA, non-citizens (legal permanent residents aka "green card" holders) can't get passports.

Is there a reason they can't get a passport from their country of citizenship?

Plus, passports are fully standardized, at least the biometric ones are. It's possible to read and verify the data on a biometric passport entirely offline using open source applications that implement the documented processes.

Presumably they can but it won't prove their legal status in the US, assuming the local government even recognises it as a legal form if ID

Greencards have a MRZ just like passports though.

Green cards are effectively entry-only passports (from the perspective of the US). You can enter the country by land with just the GC with no passport. Additionally, if you arrive by air and you have global entry they don't look at your passport at all, just the GC.

> In the USA, non-citizens (legal permanent residents aka “green card” holders) can’t get passports.

Yes, but legal permanent residents (and some other legally resident aliens) also have federally-issued ID, and its not optional the way passports are for citizens. (For LPRs, the Permanent Resident Card, for others the Employment Authorization Document or Immigrant Visa.)

Forgive my ignorance, but isn't the green card already a federally issued, nationally recognised photo ID?

Yes but they definitely have centralized id - the 'Alien Registration Card' itself. Technically, lawful permanent residents are supposed to carry it at all times.

How did the green card holder enter the USA without a valid ID / passport?

Well, they probably didn’t do so with a valid US ID, and certainly not with a valid US passport.