The broadcaster behind Who Is America?, Sacha Baron Cohen’s new TV show, has said the claim that the comedian made fun of disabled war veterans is erroneous and that Sarah Palin’s account of being filmed for the show is inaccurate.

A spokesperson for Showtime, the US channel that airs the programme, said there had been “widespread misinformation” about Baron Cohen’s character Billy Wayne Ruddick Jr PhD, a parody of an online conspiracy theorist, who interviewed Bernie Sanders in the show’s first episode.

“Baron Cohen did not present himself as a disabled veteran, and viewers nationwide who watched the premiere on Sunday can now attest to that,” the spokesperson said.

“In Sunday’s episode, during an interview with Senator Bernie Sanders, Baron Cohen in character as Dr Ruddick was asked by the Senator if he is disabled, and he stated that he is not and uses a mobility scooter to conserve his energy.

“In addition, Baron Cohen never presented himself as a veteran of the US military to former Alaska Governor Sarah Palin during the booking process or during the filming of her interview, and contrary to her claims he did not appear in a wheelchair. In both the interview with Governor Palin and the interview with Senator Sanders, he did not wear military apparel of any kind.”

Sarah Palin called Baron Cohen “evil, exploitative [and] sick” and claimed he fooled her into appearing on Who Is America? by posing as a wounded military veteran.

In a Facebook post Palin wrote: “Yup – we were duped. Ya’ got me, Sacha. Feel better now? I join a long list of American public personalities who have fallen victim to the evil, exploitive, sick ‘humor’ of the British ‘comedian’ Sacha Baron Cohen.”

Baron Cohen responded by posting a letter from Billy Wayne Ruddick Jr PhD, which read: “I did NOT say I was a War Vet. I was in the service – not military, but United Parcel, and I only fought for my country once – when I shot a Mexican who came onto my property.”

The Showtime statement came after a billboard designed by rightwing artist Sabo was erected in Los Angeles. It depicted Baron Cohen as an amputee in a wheelchair, alongside the quote: “Sacha Baron Cohen walks away with a hit ... and a touch of stolen valor.”

The term “stolen valor” refers to people who claim falsely to have served in the US military.

Sabo told the Guardian in an interview in 2017 that he believes “leftism is a mental disorder” and that he is “fighting the good fight” with his campaign of pro-Trump graffiti across Los Angeles.

“Stolen valor” was also referenced by the conservative pundit and former congressman Joe Walsh, who was also duped by Baron Cohen and claimed that the comedian was mocking disabled war veterans.

“Dressing up as a wounded veteran is absolutely stolen valor, his tactics are disgusting,” he tweeted. “I totally get @SachaBaronCohen’s gig. He’s a comedian, and he can be funny, but mocking a disabled veteran to spoof @SarahPalinUSA is a serious matter. I am just telling you what I encountered – it was much of the same she experienced.”