That's not how that law works. The safe harbor protection in the DMCA is for Youtube, not their customers. It protects them from legal action by copyright holders as long as they honor the process spelled out in the statute.
There's absolutly no law requiring Youtube to host whatever content you want them to. Nor should there be, really.
> It protects them from legal action by copyright holders as long as they honor the process spelled out in the statute.
Yes, that's what I was referring to; YouTube is now saying in some of their emails[1] about taking down a video that they are not intending to forward the counter-notification to the claimant, which they are required under 17 USC 512(g)(2)(B) to do if they want to limit their liability as a service provider.
They don't have to put the video back up or do anything when someone sends a counter notification, but that means they have full copyright liability for that video. They can now be sued directly for violating copyright for each copy they made when someone viewed the video prior to when it was taken down.
In the video in my previous comment, a copyright lawyer discusses the situation. He thinks the big music industry companies that are involved in these agreements ("YouTube enters into agreements with certain music copyright owners") must have indemnified YouTube for any legal costs they might face in exchange for the power to anonymously kill videos without question or appeal.
> They don't have to put the video back up or do anything when someone sends a counter notification, but that means they have full copyright liability for that video. They can now be sued directly for violating copyright for each copy they made when someone viewed the video prior to when it was taken down.
Anybody claiming to own the copyright. It doesn't matter if the claim is legitimate; "safe harbor" means the time and effort wasted on copyright problems is limited to hiding/restoring videos and forwarding a few legal notices between the claimant and alleged copyright infringe channel. The expensive parts like defending against potentially frivolous claims happens directly between the parties involved.
There's absolutly no law requiring Youtube to host whatever content you want them to. Nor should there be, really.