President Trump's personal lawyer, Rudolph W. Giuliani, has repeatedly suggested special counsel Robert S. Mueller III is playing a game of “gotcha,” hoping to catch Trump in some insignificant contradiction that could be construed as perjury and used against an otherwise-innocent president.

“We’re not going to sit him down [for an interview] if it’s a trap for perjury,” Giuliani said last week on Fox News.

On Sunday, however, Giuliani appeared to betray a deeper worry. The premise of his reluctance to make Trump available for an interview is that Mueller is operating in bad faith and might prey upon the imperfection of human memory to ensnare the president. Yet it seems what truly frightens Giuliani is the possibility Trump could lie on purpose.

On ABC's “This Week,” host George Stephanopoulos asked Giuliani to explain previous false statements by members of Trump's team. Last year, Trump attorney Jay Sekulow and White House press secretary Sarah Huckabee Sanders denied a Washington Post report that the president had dictated a misleading statement to the New York Times on behalf of his son, Donald Trump Jr. In a January letter to Mueller the Times obtained and published Saturday, Trump's legal team conceded the president did, in fact, dictate the statement.

Giuliani suggested the false denials by Sekulow and Sanders could have been caused by confusion. Stephanopoulos, clearly skeptical, cut him off.

“It’s not a very complicated thing,” Stephanopoulos said. “The president was there.”

“But I don’t know that Jay — Jay would have to answer that, and I've talked to him about it,” Giuliani said. “I think Jay was wrong. I mean, this is the reason you don’t let the president testify.”

Giuliani's contention is Sekulow and Sanders were wrong but not lying when they claimed Trump did not dictate the statement to the Times, which mischaracterized the nature of a campaign-year meeting involving Trump Jr. and a Russian lawyer purporting to have dirt on Hillary Clinton. It is indeed possible Sekulow and Sanders did not know, when they issued denials for the president, what they were saying was false.

But the president almost certainly knew what they were saying was false. As Stephanopoulos noted, “the president was there”; he dictated the statement and presumably remembers doing so. After all, Sanders has said it is “disgraceful and laughable” to question Trump's mental acuity, and Trump recalled the episode well enough that his lawyers ultimately corrected the record in a letter to Mueller.

So when Giuliani says “this is the reason you don’t let the president testify,” it is hard to read “this” as some kind of accidental falsehood. Giuliani and Stephanopoulos were not discussing a situation in which Trump could plausibly claim to have been unaware of the truth or unable to remember what happened; the conversation was about Trump's own actions on a significant matter — a subject on which Trump ought to be the leading authority.

Giuliani's apparent fear is the president, in an interview with Mueller, might intentionally provide false information — that Trump could, in effect, set a perjury trap for himself.