As in elections, in referenda we unfortunately cannot expect the MPs to tell us the truth. The result of course still stands, but that does not mean we have to like it - after an election if we lose do we shut up for 5 years?
What is amazing is how little planning there was for brexit - compare how much planning the SNP had done in the Scottish referendum.
A different issue is the future PM - May or Leadsom - surely any system that results in choosing between these two is by definition not fit for purpose.