Actually, it does.
You acknowledge that the statute is on the books of North Carolina.
The deputy advises the couple he’s going to cite them for violation of that statute. At that point, they are being detained – non-custodial arrest, mind you. When they shut the door on the deputy, they commited the crime of resisting arrest.
Now, you seem to be arguing that because the Supreme Court invalidated other, similar laws in other states, this particular statute is similarly infirm, and should be treated by everyone – cops, courts, public – as though it simply didn’t exist.
That is not the rule, though. The fact that the Supreme Court has struck down similar laws in other states does not erase this law from the books. Legally speaking, it exists. It may be challenged, of course, by pointing out that the same rationale the Supreme Court used in Texas v. Johnson applies equally well to this law. But that challenge is made to a judge, in response to a citation… not to a deputy sheriff.
You also seem to hang your hat on how assholish the deputy is to enforce this, as though that has some value in determing how the law ought to work. This, too, is not the rule. You can imagine a cop pulling someone over for going one mile per hour over the speed limit. It’s never done, right? Yet you would agree, I hope, that the driver doesn’t have the legal right to slam his car door and refuse to accept the speeding ticket.
In my view, the deputy is probably lying and the couple probably telling the truth. But even accepting every word the couple says as true, they resisted arrest.
Now, it appears in North Carolina that a person is privileged to use force to resist an unlawful arrest. If this is the case, and I know nothing about North Carolina law to have an opinion one way or the other on the point, then it’s likely the couple can prevail on the charge of resisting arrest. But that, too, is an argument that must be made in court, as I’m almost certain that “unlawful arrest” will be an affirmative defense to the charge of resisting arrest – meaning that the burden to prove the unlawful arrest in this context will be on the couple. (I welcome correction on that point, of course).