Twitter has been claiming it's not a newspaper or editorial organization. They are legal benefits for Twitter to NOT be a newspaper. That's why they need to claim an objective reason for censoring/fact checking a specific story.

So, I understand what you say but Twitter would beg to differ with you.

Also network effects are harder to come by in newspapers. Imagine if there was one newspaper that had 100x the readership of the second most popular one. That'd be considered a threat to democracy.

They don't need to claim any reason, they can take down any content they want for any reason.

The only legal protection they have is not being held liable for the speech of their users. Newspapers don't have that because the writers are on their payroll.

The payroll is not the reason. Libraries and newsstands and post service are free from that liability either, but they don't have writers on their payroll. Newspapers that publish readers' letters normally don't pay for that. What makes them publishers is that newspapers choose what to publish. According to the court decision of 1995 [1]:

"By actively utilizing technology and manpower to delete notes from its computer bulletin boards on the basis of offensiveness and "bad taste", for example, PRODIGY is clearly making decisions as to content, and such decisions constitute editorial control. (Id.) That such control is not complete and is enforced both as early as the notes arrive and as late as a complaint is made, does not minimize or eviscerate the simple fact that PRODIGY has uniquely arrogated to itself the role of determining what is proper for its members to post and read on its bulletin boards. Based on the foregoing, this Court is compelled to conclude that for the purposes of Plaintiffs' claims in the action, PRODIGY is a publisher rather than a distributor."

[1] http://www.tomwbell.com/NetLaw/Ch04/Stratton.html

Section 230 was written after that court decision. Yet for the law to be consistent its provisions must agree with this reasoning.

Right so it would seem Twitter is a publisher. I'm fine with that. Who wouldn't be? But whether it is or not it has the right to take down content. And I think it should do so if it thinks such content is misleading the public.

Note that there is a difference between "publish all posts" and "deliver direct messages", and Twitter is blocking the latter as well, as far as I can tell.

Depends on what you mean by "deliver direct messages".

Does it mean "deliver a direct message to one or more named recipients" or does it mean "broadcast/publish a message to the public"

The former.