There's no mandatory sidepath-use law in the NC state code.

Some municipalities have them. We cyclists in Cary, NC got Cary to repeal the one Cary had on the books once Cary got ready to build its first sidepath, which we also opposed.

The cop did not give a lawful order. He had no business telling the cyclist to get on the sidewalk unless it was an emergency. Simply being on the road isn't an emergency unless there are other issues, in which case he needs to explain why.