That matches what I have read. And the request to remove or disable material is all it takes; no judge, jury or court case is needed, just an accusation. So he with the deepest pockets wins.
This is what I understand, too (except I think some judicial review is required, but not one the owner of the website gets to attend). Basically it transitions from, “I think someone is breaking my copyright, lets take him to court” to “I think someone is breaking my copyright, take his site down and he can take me to court to get it back up”.