But in most places, that isn't the case. If there is something illegal on your server, you're going to be held responsible for it, especially if you don't have robust evidence of who else put it there (ie. a verified and accurate name and address of the uploader - something that illegal video uploaders rarely leave behind).
Even in the US, I would assume there's some practical threshold where you can't hide behind DMCA and say "I wasn't aware 100% of movies I store are copyrighted and I've acted on all requests so far".
Even if that's the case in your jurisdiction, you can spend a lot of time in jail and a lot of money on lawyers before a judge agrees with you. This is also the reason why it's not recommended to run tor exit nodes at home.
But in most places, that isn't the case. If there is something illegal on your server, you're going to be held responsible for it, especially if you don't have robust evidence of who else put it there (ie. a verified and accurate name and address of the uploader - something that illegal video uploaders rarely leave behind).