I have a theory: The NJ law may not actually stipulate the extent to which the SOS there must verify the qualifications. It could very well be written in such a way as to permit the very practice that most of the states -- if not all -- are using: trusting the political parties to have vetted their candidates.
That’s logical. And since this problem never arose before, it wasn’t anticipated. Those who were close to 0 helped conceal info also.
OTOH all SOS should verify what they are given, to illuminate fraud.