Some strange logic you are exercising here Yorkie, My understanding is that 80 per cent of the vote in the recent GE went to parties that support Brexit...using your premise thats a lot of remainers that now support leave.
As for your second part had (Remainer) Cameron actually considered that he might lose...we might not be in the situation we are now.
They don't necessarily support leave and with the Article 50 notice being served (and remember May only served it because of her own arbitrary deadline) we're into a damage limitation phase. There's a lot of pragmatism going on to try and minimise its damage with Labour offering a softer option than the Maybot.
Cameron didn't think he would win in 2015 and have to offer the referendum. Clearly he was wrong with that and with not nailing down the question. Compare the Proportional Representation referendum granted as a sop to the Lib Dems which offered just one version of PR (which wouldn't even have produced a proportional result) to the EU referendum which was granted as a sop to the Tory swivel eyed brigade but offered no one version of what Leave would look like. The flaws of the Alternative Vote system could be easily pointed out, but nailing down the flaws of Brexit was nigh on impossible because the goalposts kept moving. All the Brexit options are flawed and had one single vision of Brexit been put forward it would have been dismissed by the electorate but instead we were offered numerous different contradictory versions of Brexit which detached from reality allowed Leave to claim all the supposed benefits of leaving but deny all the downsides.
If you want to argue that as an example of incompetence I wouldn't necessarily disagree. But what is clear is that whilst some politicians who are Remain are clueless, all politicians who are Leavers are clueless. Although feel free to to name names of Leave politicians who have answers to the Brexit questions.