I agree- all the mental gymnastics about how voting again to achieve the correct result is democracy, or that democracy doesn't work, or that the previous vote is only a referendum anyway and therefore not legally binding, and so on, is really papering over the fact that the concept of rule by the people is not something to be suffered. Rule by the wealthy/intelligent/educated is what is desired, it seems.
More importantly, many layers of fascism (or economic authoritarianism) is better than fewer layers, the argument posited after the other are exhausted. Saying we need the eu is like saying we need another gang on the block. Saying we should choose the eu first is saying we should accept our place as the victims of *some* mafia organisation, so we should aim to choose the more benevolent one.
I think most people not in the comfortable and upper echelons of society might suggest otherwise; if you give me a choice I'll get rid of all of them, one by one. Obviously, that choice never was a real one, or so many wouldn't be so miffed at the vote result- it makes it harder to maintain the idea of democracy if it has to be ignored when incorrect. I suspect the same would have happened if Scotland had voted to leave the uk, but since the eu wouldn't have them (what does that say about eu motives?) they chose correctly.