> I'm pretty sharp with US employment, tax and passport forms, yet that's the first time that I've heard somebody being banned for an I-9 mistake.

Accidental false claims to citizenship are a "whoops, game over" situation which crops up on immigration advice forums from time to time. The USCIS policy manual [1] specifically mentions the I-9 citizenship question as grounds to make an inadmissibility decision, and cites relevant immigration appeals cases.

[1] https://www.uscis.gov/policy-manual/volume-8-part-k-chapter-...