In a new book, the former Trump White House press secretary Kayleigh McEnany repeats her famous insistence that she never lied to reporters, in part because her education at “Oxford, Harvard and Georgetown” meant she always relied on “truthful, well-sourced, well-researched information”.

But McEnany – who also studied law at the University of Miami – makes claims in her book which do not stand up to such assurances, for instance about Donald Trump’s support among the US military and about the severity of Covid cases among White House staff.

McEnany was Trump’s fourth press secretary, after Sean Spicer, Sarah Sanders and Stephanie Grisham. With the arrival of For Such A Time As This: My Faith Journey Through the White House and Beyond, all four have written memoirs. Grisham, who published a gossip-filled book in October, is the only one to have turned on Trump.

McEnany’s book will be published on 7 December by Post Hill Press, a conservative outlet. The Guardian obtained a copy.

McEnany gave her first briefing as White House press secretary on 1 May 2020, restarting sessions abandoned by Sanders and Grisham.

A reporter asked: “Will you pledge to never lie to us from that podium?”

McEnany replied: “I will never lie to you. You have my word on that.”

As the Guardian wrote then, “even on what proved an assured debut” McEnany “skated close to peddling dodgy information about Trump’s responses to the coronavirus pandemic (‘This president has always sided on the side of data’) and to allegations of sexual misconduct (‘He has always told the truth’)”.

McEnany now works for Fox News. She has restated her claim, telling a conservative audience this June: “And then there was the question, ‘Will you ever lie to us?’, and I said without hesitation, ‘No’, and I never did, as a woman of faith.

“As a mother of baby Blake, as a person who meticulously prepared at some of the world’s hardest institutions, I never lied. I sourced my information, but that will never stop the press from calling you a liar.”

On the page, however, McEnany often relies on single sources, anecdotes and conservative talking points. As a result she is at least, in the famous words of Alan Clark, a former British minister, “economical with the actualité”.

For instance, McEnany claims “it was no secret that the military supported Trump, overwhelmingly”, adding: “It was the job of the deep state to change that, and the press would willingly assist. They tried, but they failed.”

According to conservative conspiracy theorists, the deep state is a body of bureaucrats and intelligence agents who worked to thwart Trump in office. Steve Bannon, once a senior Trump aide, did much to popularise the theory. He has said it is for “nut cases”.

As evidence of press support for the deep state, McEnany cites a bombshell Atlantic report from September 2020 which said Trump spoke dismissively of veterans, including the late senator John McCain, and those killed in US wars, such as the son of his second chief of staff, John Kelly.

McEnany writes: “As Forbes wrote just after the story published, ‘Military Households Still Back Trump Over Biden, Despite Bombshell Atlantic Report’.”

The poll reported by Forbes showed Trump leading Joe Biden 52%-42% among military households.

But it was taken in September 2020, two months before the presidential election. As reported by Military Times in November, exit polls showed a closer split, Trump up 52-45 overall but Biden leading 51-40 among younger veterans. The outlet noted that in 2016, exit polls showed Trump beating Hillary Clinton 60-34.

McEnany also cites a conversation with “a US ranger” she says drove her home from the White House in September 2020.

“President Trump loves our troops,” she told him. “That [Atlantic] story is completely false.”

“You don’t have to tell me that ma’am,” she says the driver responded “confidently”, adding: “I know it. He was our savior after Obama.”

McEnany also writes about how Covid-19 spread through a White House which showed scant regard for social distancing and masking.

“Thankfully,” she writes, “everyone in the White House made a full and complete recovery, including me.”

Trump also contracted Covid-19, spending time in hospital. McEnany does not mention the case of Crede Bailey, head of the White House security office.

Bailey’s case was widely reported in December 2020. His family, Bloomberg News said, “asked the White House not to publicise his condition, and … Trump has never publicly acknowledged his illness”.

McEnany was asked about Bailey at a White House briefing. She said: “Our heart goes out to his family. They have asked for privacy. And he is recovering, from what I understand. We are very pleased to see that. But he and his family will be in our prayers.”

On a GoFundMe page set up to help pay for Bailey’s treatment, however, a friend wrote: “Crede beat Covid-19 but it came at a significant cost: his big toe on his left foot as well as his right foot and lower leg had to be amputated.”

In January, Bailey’s friend gave an update on his condition.

“For now,” she wrote, “Crede is wheelchair bound with the occasional use of crutches. He will eventually get a prosthetic limb but that takes time and money as each prosthetic is individualised to the recipient. Once he receives the prosthetic there will be LOTS of rehabilitation physicians, physical therapists and occupational therapists in his future as he works to regain his independence and mobility.

“… Crede’s medical team has said that he will never regain full lung capacity and it may lead to long-term breathing problems. He has suffered lasting damage to his heart and now has increased risk of heart failure or other complications and Covid-19 caused him to develop blood clots and weakened his blood vessels which contributes to long-lasting problems with the liver and kidneys. But enough of the negative!”