Around 4 million EU nationals that live in the UK, were not eligible to vote, and they are directly affected by his decision, while they pay taxes and they contribute to the economy as much as the ones who could vote ( if not more... ). Also, a significant percentage of those who voted "Leave", around 10% at least, now would certainly change their vote since they saw that "scare tactics" was basically people telling them how economy works. So a false 2% margin is "democracy"? Not really. And this decision is way to big to rely on that typical and false margin. The circumstances do matter.

Oh, by the way, "The referendum was non-binding, it's advisory".