in most states that is true, but my understanding is that nc is different. i could be wrong but i looked briefly at that issue and was surprised at the answer.
It could be that in NC the prosecutor has to agree to the bench trial as well. I'll see what I can find.
I never knew NC law was even freakier than Louisiana law...
I have looked at NC law now, and I suspect I know what you read. Some jurisdictions refer to their lower level trial court as "district," where other states use that term for major trial matters, felonies in particular. In NC, it appears there may not be a right to jury trial for misdemeanors tried in their "district" court. But there is a right to a trial de novo (anew, or new trial) in the higher level trial court as the appeal from that lower court, and such trial is subject to the right to a jury.
There is a rule that is confusing, and it does seem to say there is no right to a jury trial, but you have to read the other materials to see it's an inferior court, probably not a court of record.