Yes those are the words defining the initial safe harbor agreement well done.
I’m talking about in practice and how the dmca has actually been used. Why do you think companies like youtube entirely sidestep the dmca? They do it because the dmca is a huge drain on resources and still opens you up to litigation if you make any mistakes (like not working on the weekends for your volunteered lemmy instance that suddenly got 10,000 dmca requests from Sony pictures)