This logic works, if the referendum is won by a clear majority, if the electorate has expressed their will in line with the vote on several different occasions, or if the results at least aren't unusually far-reaching. Elections are held every few years, so such shorthand results are adequate. Joining the EU is a long process that typically lasts several election cycles, so a simple yes on a referendum is sufficient to confirm what was fairly clear all along. A referendum on starting the process to join the EU - like the one Iceland had a few years ago - is sufficient to start the process or not to start it at all.
A referendum on leaving the EU is drastically different from all of those. The electorate has expressed their will once and only once, the results were very close, and the results will be extremely far-reaching. Pretending it needs to be followed because the party in power didn't factor the possibility of loosing the referendum, even though the electorate was manipulated and it will never be given a chance to reconsider, is democratic is, well, dishonest.
McHrozni