Brexit proves that some issues should not be decided by a referendum?

The whole world watched the U.K. fence itself off of the rest of Europe in June 2016.
The nation, devided from within, found itself making a decision with significant consequences for all members of the United Kingdom. Both sides, "Leave" and "Remain" had strong campaigns, fighting for their point of view and politicians justifying the leaving of the European Union or remaining.
Immigration was, by far the most important argument of the EU opponents. Security in general, but also regarding the "War on Terror" could be more effective with EU-assistance, said the proponents.
The circumstances and the media coverage at the time Brexit was at issue, let me come to the conclusion that a referendum as such is a valuable and democratic way of making a collective decision, but if the public's attitude is shaped through the mediation of fear and sensation mongering of biased media, then it lacks impartiality and therefore is an improper way of deciding issues like Brexit.