Well, it is how the DMCA works. If the videos are uploaded by someone else (not by Udemy), then all they have to do is remove the video promptly if sent a DMCA request. If they did that, they would not be liable for damages.
Though, I will note that Udemy does have a designated agent in regards to DMCA Safe Harbor, so the OP may want to check that they submitted complains the correct place:
> Via E-mail: copyright@udemy.com[1]