I'm not actually sure of that the news media are willing to carry every message.
From where I'm sitting (In Australia) the US news media seems to be quite free and happy to limit their coverage of output from the White House. Now the news media are commercial companies and I'm guessing their thinking is that they don't want to broadcast material that their audience finds distasteful or unappealing so they limit what they broadcast.
My first reaction to the banning of the President was to wonder how I get an unedited account of what (however bizarre) he is saying and it's proving to be somewhat difficult. Maybe he's given up and gone back to playing golf so nothing is being said.
I think the media companies are in a very difficult position. Platforms like Facebook and Twitter have been placed in a position of a primary outlet for any number of public personalties and as such have a degree of moral responsibility to clearly and without alteration transmit the words of those personalities. The problems start when the personalities use the platforms and the comment systems associated with them not as a conduit for information but as a soapbox to persuade people to believe dangerous falsehoods and organise illegal activity.
The question is, where is the line drawn.
Can I post fiction on Twitter? Of course, and there are many authors who do just that, posting stories in small chunks. Can I post satire? Yep, the Onion does this regularly, with their audience fully understanding that what they read is not factual. Can I post blatant damaging falsehoods about identified people? Well yes, but I'm guessing that I could be facing deformation charges, and I'd probably be reported to twitter and banned.
So the line is drawn, post what you like, but don't cause damage with false information. This again raises the question, should the news media broadcast the words of public officials if those words are false and potentially damaging?
In an ideal world we would have a well educated public with finely tuned bullshit detectors who would be able to safely consume unedited false content, being able to determine for themselves what is and isn't true. Unfortunately in most countries we have a significant proportion of the population who are unable to determine attractive falsehood from fact which leaves the news media in the position of editing/censoring words to try to limit damage.