DMCA notices are different. They apply when a site cares about Safe Harbor. Lets say your ISP cares about claiming safe harbor so they are not responsible for YOU uploading illegal content.
The White House does not care. Sue em. So you can claim anything you want, there is nobody trying to claim safe harbor so they can do whatever.
If I am taking responsibility for all content on my site, then I am not trying to go for safe harbor, if I know none of it hits any copyright violations I will never use safe harbor and take any content down. However my ISP might take my site down if the complaint is made to my ISP not to me because my ISP does not know/care if I am hosting copyrighted content because they don't want the legal headache.