Reminder that the normal YouTube copyright process isn't the DMCA process, but instead a process YouTube came up with as part of a settlement with the record labels that gives those making the claim nearly all of the power.
The youtube TOS does not shield people making false claims from liability. It is extremely lopsided in every other aspect, though.
But the DMCA section about liability for false claims doesn't apply if it wasn't a DMCA takedown in the first place.
There are other actionable laws that could potentially be used here though. Slander of Title [1] certainly seems to apply here, given that the claims disparage ownership, and could be argue to have caused damages, through things like unwanted ads being played before and during the videos.
Which doesn't come with attorney's fees by default. So if they screwed you out of, say, $10k, it might not even be worth it to go after if there's a large disparity between your resources and theirs.
You don't need the DMCA to be able to sue someone, this is just tort law.
No, the section where you agree to binding arbitration does.