the inclusion of "including with then-candidate Donald J. Trump" reflects language added since July
Trumps Two Denials Could Provide Reason for Mueller to Demand an Interview
https://www.emptywheel.net/2018/11/28/trumps-two-denials-could-provide-the-excuse-for-mueller-to-demand-an-interview/
According to an updated NYT story on this weeks Paul Manafort and Jerome Corsi developments, the delay in Trumps submission of his open book test came in response to two things: Seeing a reference to Roger Stones regular contact with then-candidate Trump in Corsis draft statement of the offense and learning that Mueller had informed Manafort he had caught him lying.
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Remember, the GRU indictment described Stone as a person who was in regular contact with senior members of the presidential campaign of Donald J. Trump, so the inclusion of including with then-candidate Donald J. Trump reflects language added since July. Recall, too, that Stone at first complained about that description, insisting that My contact with the campaign in 2016 was Donald Trump. I was not in regular contact with campaign officials, only to backtrack to, I certainly acknowledge that I was in touch with Trump campaign officials, when he realized the implications of that. As CNN notes, in recent weeks Muellers team asked for records of Stones calls and visits to Trump Tower. So its possible a recent witness Michael Cohen and Steve Bannon could both be possibilities suggested that Stone had conveyed WikiLeaks information directly to Trump, leading to the request for more records.
And (as I used as a hypothetical last night on Chris Hayes show), we know that Manafort and Trump met on June 7, 2016, just before Trump announced an attack on Hillary Clinton in coming days and two days before the June 9 meeting.
So it is quite likely Mueller has evidence that both of Trumps claims are lies.
Finally, remember that one excuse Trump has given for refusing to sit for an interview is that none of this really affects him directly, so Mueller has no need to engage in back-and-forth with him. Its quite likely that a Corsi indictment and a Manafort sentencing report could be public within the next month alleging that both of the claims Trump made are false. While I still doubt Mueller would wait for a Trump interview, any inconsistency between Muellers evidence and Trumps answers would make it far easier to demand an interview.