You are probably correct about the location, although Federal provost officers weren't particular about exactly where a POW was captured.

It's difficult to say where Early went wrong in terms of battlefield management. His army went into action woefully outnumbered, and by the afternoon of October 19th, most Confederates had been without sleep for roughly thirty-six hours and hadn't eaten since the night before. A couple of things could have happened to seal the deal for the Confederates at Cedar Creek, but Early had no control over either of these factors.