[akersten]

There is no "admission you're a publisher," it's a meaningless concept with respect to the laws that are on the books. The law is: hosts of user-generated content can remove that content at their discretion, and still not be considered the "speaker" of all the other content they do not remove (obviously, because that would be impossible to police at scale, and obviously because obviously Twitter did not make the post).

If you kick someone out of your restaurant for being loud and boisterous in the dining area, you are not suddenly responsible that someone was disparaging a public figure the next seat over and you chose not to kick them out.