This was imposed before the fact and by a Brexiteer no less. Whether I like it or not, he was technically correct.
However, retaining the focus on your article. The European Union Referendum Act 2015 was an advisory referendum, enacted and executed at national level, without ward boundary representation, which naturally introduces a need to sample the populace as a whole and so, unlike constitutional breakdowns, randomising it.
Plus, there is a null hypothesis. What is wrong with “The difference between the Leaving and Remaining is materially zero” or “The UK population does not want to Leave the EU”? Forming a null hypothesis, whilst not always easy, is relatively trivial. You then need to run the experiment and analyse the result, to a point where the result falls outside the 95% or 99% confidence intervals (or otherwise deliver a small-p) to be considered significant. Let’s not forget the principle of the basis of statistical significance. It has to materially beat chance. If it fails to do that, it fails to disprove the null hypothesis.
With a wide enough sample, such as we got with the size of the voting population who engaged, this now turns the control into a very close randomised position, which is the real quality of the sample you should be referring to. That basically means a coin. 50:50. In a 50:50 random vote, at that level, the 95% confidence interval is between 40 and 60 in every 100. Hence, even taking a 55% super-majority vote wouldn’t have met the threshold to reject the null hypothesis. Because the results were as good as random, it did not provide a mandate to state that leaving or even remaining was chosen by voters. It stated it is no different to random. The only reason it is the status quo is because we are currently in that position.
Hence, the flip side to your argument against the status quo, is that going against the science prejudices real results in favour of chance, which not only is wrong, it is also downright dangerous. You may as well flip a coin.