The more I think about this, the more I'm wondering if May and everyone else in government actually wants to avoid Brexit completely.
If we look at that infamous pie chart showing that only 26% of the adult population (or 37% of the registered electorate) voted for Brexit, and taking into account that most people who really wanted it would have made the effort to vote, and that some people openly voted for it to piss off the government, there really isn't a massive demand for Brexit.
It's not unreasonable to suggest that a re-vote might be for Remain.
I know politically that would be a disaster for the Conservatives - they've made their bed, they will be lying in it for a long time whether Brexit goes ahead (an economic disaster) or is cancelled (a political failure). If they can now push the blame on everyone else (the DUP, Europe, Ireland, whoever), they can try, whichever way Brexit goes, to hang on to their core voters. If they admit now that they cocked up and haven't a clue what they are doing they will lose that vote too.
So this all seems to me to be political obfuscating, just trying to confuse everyone enough to take the heat of the people who are firmly to blame in all this. Cameron, obviously (but he's disappeared), Boris (but he's made of Teflon), and May, who we are all meant to feel a bit sorry for, because she's the one left holding the baby.