If they're charging $$ to watch the videos, they can pay someone to review content... in this case, Udemy could very well be liable for penalties beyond DMCA safe harbor.
If you'd like an example, Banks won't even OPEN an account in states that have legalized recreational marijuana, simply because it's still illegal federally, and they're avoiding liability.
I just thought I'd share, since I have firsthand experience in that particular industry (online payment processing).
I'm not saying they are immune to everything, just that the accepted and realistic option for any service that accepts user provided content is to handle takedown requests. It does place the burden on the copyright owner but it's the process we have so if Udemy or anyone else does follow this accurately then what is the problem?