At the absolute minimum the moderators have to actually be able to watch the run, and ideally everybody else can watch the run too. Private's no good, Public or Unlisted is fine.
No, you cannot use a run from a private YouTube channel without the owner's permission. Private YouTube videos are not publicly accessible, and they are restricted to specific individuals authorized by the video owner. Therefore, using content from a private YouTube channel without the owner's consent would likely violate copyright and intellectual property rights.
If you intend to use content from a private YouTube channel, it's essential to reach out to the owner and request their permission or discuss potential licensing arrangements to ensure you are adhering to copyright laws and respecting the content creator's rights. Always respect copyright and intellectual property laws when using content from YouTube or any other platform.