Military records for the 16th North Carolina are as complete as any you may hope to find from 1861 through the end of 1864. That being said, there is no evidence that anyone named Hyder or Hider &c ever served with this regiment. However, since Capt. Davis was a Rutherford County resident, it's quite possible that William Hyder may have known and admired the man. Many pension applications include claims that cannot be supported by evidence available, especially those filed many years after the war ended. I would suggest that you review the pension application carefully for specific details of service for further examination and research.