I also am not a lawyer but from what I understand the situation is actually more severe than that.

I couldn't find the reference offhand but I've read that YouTube has no ability to adjudicate the validity of a DMCA takedown request at all. They must responed as proscribed by the DMCA.

Which makes sense because once the DMCA is involved it's ultimately a legal dispute between the person that uploaded the video and the person that claims to own the copyright. And that kind of dispute is something only the courts can decide.