Youtube doesn’t know, because the DMCA doesn’t require the complainant to be very specific. The right course of action is to deny the complaint and make a counter complaint to youtube. This forces Youtube to reinstate the video, and forces the original complainant to take their complaint to an actual court. A copyright bully will simply never do that. They’re relying on people to give up at the first step, without making a counter complaint.
YouTube's system has nothing to do with DMCA.
You can also use this mechanism, but their "Content Protection" system has no legal requirements.
Does YouTube do put-back if you file a counter-complaint? YouTube says they do.[1]
[1] https://support.google.com/youtube/answer/2807684?hl=en