The DUP has issued a curious rebuttal to a well-sourced story in today’s Times on its leadership’s openness to a Brexit solution involving a customs union or single market membership.

Senior sources within the party tell the paper that they could support a “softer Brexit, as long as it applied to the whole United Kingdom”. Neither DUP MPs nor Arlene Foster, their leader, are shy of articulating this position in public.

Foster in particular has been more than willing to stress that ultimately, her party has only one, inviolable red line – that the whole United Kingdom exits on the same terms – and that all else about the shape or hardness of Brexit is secondary. She even said so in an interview with the Times in November.

But notwithstanding the fact that it reflects her own stated position, Foster has described this morning’s story as “inaccurate and no doubt intended to undermine efforts to get the necessary changes to the Withdrawal Agreement” and “an attempt to cause division”. She adds: “For the future we want an agreement which returns control of our money, our laws and our borders through a UK-wide trade agreement with the EU.”

Though written as if it were a denial, Foster’s rebuttal isn’t and cannot be one, for the obvious reason that it is true that she and her party could accept a UK-wide soft Brexit. It is instead designed to protect the DUP from the political consequences of the division she says the story is an attempt to foment.

Tories have long suspected, with some justification, that nobody in the DUP is particularly doctrinaire about the politics of EU withdrawal apart from Sammy Wilson, its pugnacious and Farage-aligned Brexit spokesman – described by one colleague as “the Jacob Rees-Mogg of Northern Ireland”, such is his outsized role in the debate.

Downing Street made the mistake of thinking this equanimity on the specifics of Brexit extended to the Irish backstop, and believed that, when push came to shove, that it could convince every DUP MP but Wilson to abstain on the meaningful vote. It couldn’t, as the implications of the backstop for the integrity of the union as they see it is something all ten DUP MPs and indeed Ulster unionism as a broader movement do agree on.

Beyond that, however, there is much less consensus on, still less a fierce attachment to, a particular vision of Brexit. That poses a political problem for the DUP at Westminster. The easiest way that Conservative Leavers in the European Research Group could have got the high-divergence, Canada-style Brexit they crave would have been by jettisoning their confidence and supply partners, and accepting the need for a regulatory border in the Irish Sea.

The DUP's advocacy for a hard Brexit must be seen in this context. It is less about genuinely sharing the enthusiasm of the ERG for the cleanest possible break with Brussels than it is convincing them that they won't rat on it. As long as that reliability isn't in question, Tory Brexiteers won't rat on the DUP and accept that Northern Ireland is the price for Canada. This is exactly why the party's obstructionism and guerrilla tactics against the government in parliament have been aided and abetted by Conservative opponents of the withdrawal agreement.

In the immediate term, Foster’s objective is making sure that her definition of “the necessary changes to the withdrawal agreement” is the same as the ERG’s – time limiting or binning the backstop. The last thing her party needs is for Tory Brexiteers to sense betrayal and demand a return to what the EU were originally willing to offer: one that applied to Northern Ireland alone. This truth of Commons arithmetic, rather than belief in Brexit as an end in itself, is what will stop them backing a customs uion. Their strategic interests will not be served in pursuing something they could live with but the Conservative Party as an entity could not - like a customs union. That would almost certainly end this parliament, and their unprecedented leverage, for the sake of a Brexit that mightn't pass anyway.