You’re correct. NWOHR passports don’t confer full citizenship upon the holder. Simply reporting what I know: The children’s mother is a citizen with household registration (that may make a difference when dealing with kids), and the school personnel said “good thing they have these Taiwan passports, otherwise we couldn’t enroll them.”
Also, my wife is a local. I don’t think she has any special guanxi, but it may just be a case of “different rules for thee and me.”
The school may not know what they are talking about.
But if the mom is a proper full citizen, kids can get an ID and enrol in school. If they don’t have one, and the school is just not well educated on the system, probably don’t mention too much. You cna probably skip by, with dumb administrations, showing the mothers paper work and hope they aren’t diligent in doing their job.
Though we have had straight foreigners come and attend schools here, it just won’t count for anything officially. More like there is an open seat and the admin are OK with the liability risks.