He hasn't unequivocally backed a public vote though, he's still saying he only backs one if a managed deal with the EU can't be reached. That isn't the same as properly backing one.
As
@Smores says the goal of the party is not be a cheerleader for tiny section remain people. Corbyn wrapping himself in a EU flag and representing the views of the people on Remain marches doesn't actually change anything.
Look if the ultra remain people were serious, they would have joined the labour membership after 2016 and try to democratise the party with the goal of changing labour Brexit position. But what they've instead done is complain and moan on twitter about politicians not meeting their every cultural preference(Liberal have turned into the left of the past).
And scepticism is warranted. If Blair had been on the verge of losing in, say, 2005 but had promised a more leftist platform in order to get elected, would you have actually believed a word he'd been saying? You'd have been completely justified in not buying into him.
Mate I wouldn't be voting for Blair post 2002.
But who said not to be sceptical ? But had Blair made similar left wing moves as Corbyn has done to Remain, I would have considered it a win for the left but in the end my answer will always be the same, it doesn't particular matter because without a democratised party everything else is pretty much useless.
They presumably didn't want to do that because the membership is overwhelmingly pro-Remain and would've immediately put pave to any of Corbyn's pro-Brexit whims.
Pretty much but had there been a democratisation of the party since Corbyns time(Which the left have wanted but the Labour Right/PLP/Union don't) then the actual position the party took would have been far more difficult to justify.