There were a lot of denials in Jennifer Arcuri’s interview on Monday morning with Susanna Reid and Piers Morgan – who single-handedly tried to play both good cop and bad cop. But few of them were meaningful.

Arcuri denied that the “friends” who said she’d had an affair with Boris Johnson were actually her friends. She denied that she would have “gabbed” to them, even had they been, and denied that any of the public money flowing into her successive startups was influenced by her relationship with the then mayor of London, whatever that may have been. Both have refused to deny that it had been a sexual relationship.

Before he became PM, sex was already 'priced in' with Boris Johnson – voters knew what to expect

“I think we’re forgetting that Boris is personable,” she announced, as if he were a labrador and it was impossible to tell whether he was humping you or saying hello. “It wasn’t like he singled me out,” she continued, which, if it was meant to indicate “he shagged everyone”, was definitely novel.

She didn’t want to be “dragged into this horrific scandal”, which she’s already in the middle of, and she didn’t want her answer to be “weaponised”, which is what they call it in the new politics when evidence of behaviour is actually used against a person in a debate about the way they behave. Finally, “I’m not answering,” she concluded, “because the press has made me this objectified ex-model pole dancer.” Ah, the pole! Only five minutes earlier, it had been just a bit of marketing genius, and also great for working her core muscles; now, after some quick rhetorical jiujitsu, the very attention she’d been seeking for her brand was suddenly part of a patriarchal conspiracy. So on feminist grounds, she could take no further questions.

If the purpose of this interview was to clear the prime minister of impropriety, it didn’t even try. If it was to clear Arcuri of dishonesty, it emphatically failed, as she openly admitted lying to the alt-right journalist Milo Yiannopoulos, before going on to spray “fake news” accusations at the rest of the press. If it was meant to bring any clarity to the events, foreign trips, public money and “IT lessons” being exchanged mainly between 2012 and 2013, it failed. It was both utterly murky and boringly transparent. It made no sense because it wasn’t meant to. Prior to the interview, we had a constitutionally dishonest man denying this rumour, among others; now we have a woman refusing to deny it on the grounds of ersatz emancipation. Impossible to say whether this makes it more likely to have happened or not, but in a sense that isn’t the question. The only interest now is in what will stick.

Play Video 0:37 Boris Johnson refuses to answer questions about Jennifer Arcuri – video

Before he became prime minister, commentators observed that sex was already “priced in” with Johnson – voters knew what to expect. Extreme negligence around its consequences – being unable to number your own children, say – was also priced in. Adultery, divorce, skeletons in closets: this is a man whose relationships are so sketchy no one knew for sure who he’d move into Downing Street with, having got there on the votes of a narrow but trenchant constituency who didn’t care.

And actually, a lot of people don’t care, and never have, about any politician’s personal life, being periodically rushed into having a reaction by pearl-clutching tabloids when the time for a scandal was politically expedient. Johnson has always banked on this, and always been proven right. Pre-Harvey Weinstein, it is unlikely that even groping allegations would have gained any traction. (Since Weinstein, of course, we have collectively, culturally managed to refine our idea of a private life: it can’t be called private if not everyone agreed to it. This is a start.)

Jennifer Arcuri: five unanswered questions after TV interview Read more

Indeed, prior to Arcuri it would have been hard to imagine the sex-related scandal that could have touched Johnson: when your entire self-fashioning is that you shag around, any further suggestion of the same is just proof that you are who you say you are. It is a unique distinction of the prime minister’s that his carefully crafted image, built on mischievous lies, turned any fresh untruths into proof of his authenticity. I say “distinction” without admiration but with a certain awe: veracity, if not sexual propriety, was always held to be key to high office. To jettison the requirement was stunningly radical.

Plainly, though, this is a scandal that won’t dissipate in a hurry. It has nothing to do with Arcuri’s dancers’ pole or even her Bavarian dirndl. The obvious problem is the suggestion of corruption: misuse of public funds, of public platforms, of trips undertaken on behalf of the British taxpayer. He has denied any wrongdoing.

Every time these details are waved away the impunity is underlined: there is, it turns out, a concrete difference between the vows taken between two private individuals and the codes of conduct undertaken between politicians and the state. It’s the difference between Johnson’s girlfriend, Carrie Symonds, slipping seamlessly into the centre of the Conservative party conference and Arcuri being unable to pass into history. Ultimately, these codes have meaning beyond trust and convention – they can be investigated and enforced. This is the hard edge where hustle meets its limits.

Curiously, Arcuri herself – contrary to her own rationalisations – is not the focus of any of this ire. Scrabbling after public money, gatecrashing trade trips, these are all behaviours we’d expect of a young startup in a hurry. She’s protected by the same Ronseal as Johnson himself, doing what it says on her tin. But nowhere on Johnson’s tin does it say, “fails to declare information in the public interest”, and this case won’t die until the details have been hammered out.

• Zoe Williams is a Guardian columnist