Theresa May at the European Summit in Brussels, Belgium. Photograph: Photonews/Getty Images

Poor Cordelia Gummer. It’s a quarter of a century now since her politician father, John, publicly fed her a burger to quash public fears over mad cow disease – and she is for ever fixed in our minds as a tiny girl in an Alice band, symbolic of everything people most distrust about politicians.

The beef industry eventually recovered, but public confidence in politicians and in their management of risk did not. When they tell us everything’s going to be fine, we don’t swallow the story like we used to. Which brings us to the mysterious affair of Theresa May, and whether or not Brexit is safe to eat.

On Tuesday this paper published a secret recording of her addressing bankers at Goldman Sachs last spring – back in the mists of time when she was still home secretary, and Brexit was still officially a disaster. Companies might look to leave Britain if we were outside the single market, she told the assembled suits sternly, plus there were “benefits in security terms” of staying.

And if just over 2% of Britons had voted differently on 23 June, perhaps she’d be saying that still. But they didn’t, so she isn’t, and now apparently it’s fine to eat this delicious lump of minced offal that six months ago supposedly risked making us sick. Do keep up at the back, everyone.

Just to recap, for those who understandably find this confusing: Britain’s foreign secretary, Boris Johnson, campaigned for Brexit but was suspected of wobbling privately towards remain. Our leader of the opposition, Jeremy Corbyn, campaigned for remain but was suspected of wobbling privately towards leave. And our prime minister was presumably either faking it in front of the Goldman Sachs faithful, or is faking it now when she insists that hard Brexit will be a rip-roaring success, or is secretly in two minds about the most totemic issue of the day – but dammit, the British people ordered a burger, and that’s what they’ll get. And we wonder why people don’t trust politicians.

Her friends will say, of course, that this tape simply confirms what we already knew. May dutifully backed remain when her prime minister asked her to do so, before transforming magically into a super-Brexiter when occasion demanded, like Lynda Carter going into a spin and emerging as Wonderwoman. (If nothing else, it’s clear why May was so resistant to making public appearances for the remain campaign in the spring, to the screaming frustration of Downing Street; she presumably anticipated her words being later used against her.)

But the fascinating thing is that if you compare the recording of May trotting out the pro-European line then with her rather different script now, it’s surprisingly hard to tell which one sounds fake.

Former agriculture minister John Gummer and his four-year-old daughter Cordelia, tucking into a beefburger at the East Coast Boat Show. Photograph: Jim James/Empics

Even Johnson, who famously wrote one newspaper column arguing for Brexit and one against it before settling on the former, couldn’t manage that. His unpublished ode to Europe, salvaged from the bin for a forthcoming book on Brexit by the Sunday Times journalist Tim Shipman, arguably goes some way to restoring the old rogue’s reputation because you can feel his heart wasn’t really in it. But the sphinx-like May sounds equally inscrutable whichever way she’s arguing.

Nobody wants to hear that fudge and obfuscation, ambiguity and half-truths – not to mention a willingness sometimes to tell different stories to different audiences – are as essential to the political process as principle and passion. But it’s true all the same.

The Tory-Liberal Democrat coalition wouldn’t have survived past Christmas if David Cameron and Nick Clegg had been tub-thumping conviction politicians; it worked only because neither of them is particularly tribal, often to the fury of their respective tribes. Theresa May is a very different character, but her natural reserve can make her something of a blank screen, on to which others project what they want to see – one way, perhaps, of managing a government that is essentially a coalition of diametrically opposed views over Brexit.

Two years ago I spent weeks researching a profile of May as a prospective Tory leadership contender, and the hardest question to answer was what she thought deep down about Europe. The consensus among old friends was that she just wasn’t all that interested in what for many Tories was an existential question, so the modernisers’ aversion to banging on about Europe suited her just fine.

But if it came to it, most thought she’d be a pragmatic if hardly enthusiastic inner. True, she’d become increasingly hardline on immigration at the Home Office and picked up quicker than most on the boiling anger of white van man, but as an ex-banker the economic case would prevail.

And that’s still what much of Whitehall assumed when she came into No 10, promising that the will of the people would be sovereign, and that Brexit really would mean Brexit. When she brought back David Davis and Liam Fox, some even wondered if this was all part of a cunning plan to give hard Brexiters just enough rope to hang themselves.

But increasingly it’s dawning on everyone that she actually means it. There is no Plan B. (If Nicola Sturgeon, Scotland’s first minister, is to be believed, there may not be much of a plan full stop.) The chancellor, who has been explaining the economic risks in the inconvenient way chancellors do, looks increasingly marginalised inside a squabbling cabinet. No wonder an increasingly jumpy City is starting to fight for its own survival.

If May really is a closet remainer, trapped in the political equivalent of a hostage video, one almost feels sorry for her. But nobody forced her to run for leader, and now it’s time to lead.

The Goldman tapes do not, in themselves, make May a hypocrite. Only she could do that – if she sought to pretend that everything she said is no longer true, or that the downsides of Brexit will, like fairies, magically die away just because 52% of voters don’t believe in them. Every decision has problems and consequences, which we elect politicians to analyse and overcome: odd that it’s only in the case of Brexit that it’s deemed undemocratic even to mention what might go wrong. Never mind the detail; swallow this.

But May should remember that the mistake John Gummer made all those years ago wasn’t just to drag his daughter into politics. It was to treat the rest of us like children, incapable of understanding the risks for ourselves.