Opinions are like fingers; most everyone has a handful or two.
NEMA has no more standing than you or I. Their papers and standards are simply opinions. The only difference is that others are more likely to grant that NEMA knows what they're talking about.
If you're trying to persuade someone, it's nice to be able to show them that you didn't just make things up, and that your opinion is shared by folks who have no part in your particular dispute.
Follow up to an incomplete post:
Back around 1985, Congress passes a law that strongly encouraged government agencies to adopt existing industry standards, rather than write their own. While this law simply codified what was already a common part of legislation (for example, the original 1972 OSHA legislation refers to the NEC), it gave a real boost to the creation of trade organizations.
It's very possible that some agency, somewhere, has adopted a particular NEMA standard for their purposes. This makes it 'law' for that agency .... but a law they can easily decide to modify or drop.
It's also very possible that there are multiple trade groups lurking in the background of any issue. Say 'pool pump' and you have the pool makers, the pump makers, and the motor makers all waiting to chime in.