The third tweet contains the real mystery. Trump claims that Mueller has a contentious business relationship with him. He additionally argues that the fact that he interviewed Mueller to replace James Comey as the FBI director should preclude him from leading the probe.

This represents a surprising new interest in conflicts of interest for the president, who has pooh-poohed concerns about conflicts of his own at every turn, including refusing to divest from his substantial personal holdings. (A federal judge last week allowed a lawsuit centered on his conflicts to proceed.)

Even if his newfound concern was sincere, it doesn’t stand up to scrutiny. It doesn’t make sense that Trump would have a personal dispute with Mueller so hostile that it would preclude his work as a special counsel, but not so hostile that it prevented Trump from considering him for an important job.

And what is the supposed “nasty & contentious relationship” the two men share? Trump didn’t say, and appearing on CNN Monday morning, Giuliani refused to elaborate. He claimed that he didn’t know, and that if the president didn’t explain, it was incumbent on Mueller to do so. Of course, lodging an accusation like this without offering any substance is just innuendo. As Giuliani, a former prosecutor, knows well, the burden of proof is on the prosecution.

The most likely bet is that what Trump is talking about isn’t new at all. The president reportedly tried to have Mueller fired in June 2017, citing an old disagreement over fees at a Trump golf course in northern Virginia. But if that’s one of the “conflicts,” it’s a trifle. As The Washington Post reported in January, “The dispute was hardly a dispute at all. According to a person familiar with the matter, Mueller had sent a letter requesting a dues refund in accordance with normal club practice and never heard back.”

As it happens, the Justice Department has guidelines for what constitutes conflicts of interest—not just interpersonal issues, but donations to campaigns as well. There’s no public evidence that Mueller and his team haven’t followed them. Moreover, Giuliani admitted that he assumed that Mueller had disclosed the mystery conflict, be it golf-related or something else, to Deputy Attorney General Rod Rosenstein when the special counsel was appointed.

It’s not unusual for Giuliani to undercut the president’s case during his interviews, including in recent media appearances. His extended chat Monday with CNN’s Alisyn Camerota was no different. Hearing a conversation with Giuliani makes the president’s speaking style seem linear and coherent by comparison, but at several moments the lawyer made notable comments.

For one, Giuliani essentially admitted that Trump’s strategy for grappling with his legal headaches is distraction.

“When you’re getting beaten up by all kinds of anonymous tweets coming from [Cohen’s lawyer] Lanny Davis and Cohen, and you put out something like that, you have every right to say, ‘You explain it, Mueller. Stand up and be a man,’” Giuliani said. The performative machismo here aside, the Cohen case is in New York and is separate from the Mueller case—so Giuliani is highlighting how the attacks on Mueller are a misdirection.