I agree with you, with one caveat. The caveat is that the referendum is, legally speaking, a glorified opinion poll. Unlike an election for political office, the results of the referendum have no legal significance. Legally speaking, the UK government has to invoke Article 50 of the Lisbon Treaty for anything to actually change. At any time, the government could simply state that there was not a clear mandate for a change and reject the results, or go ahead and hold another referendum (though either action could be political suicide at this point).
In any event, holding the referendum the way they did was simply breathtaking in its stupidity on the part of the PM and his government.
I heard a political scientist talking about this on NPR yesterday. He stated that it was lunacy to set up a situation where 43 years of treaties and trade agreements could be reversed by a simple majority vote in a glorified opinion poll by the general public. The general public simply does not have the background or the full picture to make an intelligent decision.
This is why true direct democracy (as opposed to representative democracy) is a recipe for chaos. Even the ancient Athenians realized this, which is why they set up a balance between the Assembly (where direct democracy was exercised) and other governmental institutions.
In a representative democracy, the people elect leaders who are expected to make good decisions, and who are then responsible for the consequences of those decisions. If you hand a major decision over to the people, especially one that basically boils down to maintaining or rejecting the status quo, some people will vote to make a change simply as a protest vote – even if what they are protesting has nothing to do with what is actually being voted on.
The whole situation was a recipe for disaster from the start, and should have been better thought out from the beginning.
If it was decided that a referendum was necessary for political reasons, at a minimum a high bar should have been set up from the start, which should have included a supermajority requirement for any change to the status quo.