Roger Stone buddy, birther propagandist, swiftboater, and Harvard Ph.D. Jerome Corsi has had a busy week. After saying Monday that he would reject a plea deal that would involve admitting to perjury because “I am not going to sign a lie,” Corsi has also said that he has a joint defense agreement with President Trump.

The new claims come from a book written by Corsi and obtained by the Daily Caller, the conservative website. In the book, the Daily Caller reports, Corsi says he got “limited immunity” from the Mueller team in order to talk freely about a “ ‘cover story’ he claims he crafted for Trump confidant Roger Stone.”

Federal prosecutors suspected that Corsi could be a connection between Roger Stone and Wikileaks, CNN reported.

Corsi says the cover story was specifically designed to account for Roger Stone’s now-infamous 2016 tweet that it would soon be Democratic operative John Podesta’s “time in the barrel,” posted shortly before Podesta’s hacked emails were released to the public.

The Daily Caller reports that Corsi told the Mueller team that “he and Stone hatched a plan in which Corsi would write a memo about [John Podesta and his brother Tony] to allow Stone to cite it as the basis for his tweet.” If true, that would contradict Stone’s own testimony that his tweet about John Podesta was inspired by “opposition research on the Podesta brothers’ business activities.”

But there are reasons to doubt Corsi’s new statements, especially his claim that he has an agreement with the president and his legal team. According to the Daily Caller, the book says “that his joint defense agreement with Trump’s legal team was intended to be kept from public view” and that one of the president’s lawyers, Jay Sekulow, “suggested the agreement could be verbal in nature and did not need to be put in writing.”

Joint defense agreements allow lawyers for different subjects of an investigation to communicate with each other under attorney-client privilege. Trump and Paul Manafort have such an agreement. Rudy Giuliani, Trump’s attorney, has said that his team and Manafort’s lawyers have had “open communication” and that the communication would “all be attorney-client privilege, not just from our point of view but from theirs.” Corsi writes in his book that his agreement with Trump allowed their lawyers to share information about Mueller’s line of questioning. Corsi says he used the arrangement to warn Trump “NOT to give in-person verbal testimony to Mueller under any circumstances,” fearing a “perjury trap.”

As for Corsi’s claim that Stone engaged him to fabricate a paper trail to explain the potentially incriminating Podesta tweet, Corsi apparently doesn’t have any documentation. “I have no precise recollection of that phone call,” Corsi wrote in the book, “but from what happened next, I have reconstructed that in the phone call Stone told me he was getting heat for his tweet and needed some cover.”

Stone told CNN on Monday “I never received advance notice, from anyone, that Podesta’s emails had been ‘nicked,’ as the Brits would say, and would be published.”

Corsi’s own claim is that he helped Stone cover up a bad tweet but that there was no crime. “So, what if Roger Stone used my cover story to testify before the House Intelligence Committee. Roger could amend that testimony and Congress rarely pursues anyone for criminal charges of perjury,” he wrote in the book, according to the Daily Caller. “Without the link to Assange, there was no ‘Russian Collusion’ that could be pinned on Roger Stone.”