I am not quite sure what your question is...but I will assume: is this legal. Yes.
NC is a right to work state meaning you can be fired or disciplined for any purpose. So far you haven't described anything that amounts to harassment. There may be other facts that you haven't disclosed yet, but it is very difficult to show harassment with an employer unless a hostile work environment has been created.
As to the meeting, there is no requirement that you be disciplined in private. In reality, you can be reprimanded or disciplined with every employee present. Most reputable companies won't do this, but it is legal to do so.
