And on Sunday, shortly before Corker's tweet, Office of Management and Budget Director Mick Mulvaney also weighed in on that information flow. He told "Meet the Press" that before Kelly came on board, Trump was getting information that "just wasn't ready for the president":
"MULVANEY: What I can tell you has changed is the flow of information to the president, the flow of information from different people, from different sources. It is a much more orderly and aligned West Wing than it was previously. And I think the president is extraordinarily well-served by that - and, more importantly, likes it. I was surprised to hear you say in your intro that folks are talking about John Kelly leaving. That's the very, very first I've ever heard that.
"CHUCK TODD: I only ask it because it got sparked in a story on this. I guess let me ask you this: was the president getting bad information before? Was that an issue? When you said the flow of information, was he getting bad info?
"MULVANEY: It wasn't bad info. It just wasn't ready for the president.
"TODD: Contradictory?
"MULVANEY: Not contradictory. Folks would wander in. You've heard there were several stories - and those stories were actually true - about folks would just come in and there was an open-door policy and they could wander in and talk to the president about anything. That's probably not the most effective way to get information about very, very complex issues in front of the president of the United States. So what John has done is really refined that flow of information, so that we know, before the president sees it, it's right, it's accurate and it's ready for him to act on."
Mulvaney's comments are certainly more diplomatic than the rest, but he's also talking about the president of the United States here - and he's talking about him as if Trump can't process information well unless it is sufficiently narrowed and tailored to him. And his and Bannon's characterisations of Trump's level of informational sophistication confirm all kinds of previous (anonymously sourced) reports that suggested Trump is highly susceptible to what the last person he spoke to has told him and needs constant minding. Wars have reportedly been fought in the White House over who can tell Trump what - as if he can't decide these things for himself.
Also important here: the four people we're talking about. This is one of Trump's top Cabinet secretaries, his former top White House strategist, a leading adviser on tax and budget issues in Mulvaney, and the chairman of the Senate Foreign Relations Committee in Corker. Corker's Tennessee colleague, Senator Lamar Alexander, R, once said Trump was closer to Corker than any GOP senator.
"There is no senator - no Republican senator - who President Trump talks to more than Bob Corker," Alexander said in late August. "I know that for a fact."
Perhaps Corker's comments could be dismissed as a personal feud - the comments of a senator who isn't running for re election and doesn't have to deal with the consequences of knocking the president. But the totality of these remarks doesn't paint a flattering picture of the president at all, and they come from people who would know best.