And yes, Cornwall voted leave, despite being dependent on EU funding, EU farming subsidies and EU tourism for having any sort of economy at all. Even the CLA (Cornish Landowners Association) was trying to persuade people to vote remain.
There are reasons for this, though-
-Firstly, a lot of Cornish people tend towards insularity, not just racism or Xenophobia but not even liking people from other parts of the UK. In some towns, if your family haven't lived there for generations, you'll always be an outsider.
-Decline in traditional industries of farming, fishing and mining due to cheap imports. For some people, if we could "go back to the way it was" in the 1920s or whenever, things would be better (personally, I don't think they would be, but to some this is the answer).
-Relating to this, specific issues relating to the fishing industry (which is still an employer) politicized and blamed on the EU by certain local politicians. The actual situation is a lot more complicated, and the government could do a lot more to help small fishermen, but they won't, and until recently, the EU has been a convenient scapegoat. Things won't get better, but I can see how people think they might.
-We do get a decent amount of tourism from some other EU countries (like Germany) which obviously does help the county a bit. However, most tourism jobs aren't great (usually highly seasonal and poorly paid) and a lot of people resent the idea that the county is fine because tourism. They also resent the attitudes of some tourists who e.g. struggle with driving down small lanes, aren't good at dealing with livestock etc.
-Demographics. Less young, well educated people, as there aren't the jobs/careers for them. Less professionals. More older people/retirees. If you look at the demographics of Cornwall and those who voted leave/remain, the demographics of Cornwall reflect the type of people who were more likely to vote leave nationwide.
-Lack of publicity about how EU funds have been used. People are sort of aware they exist but often think they only go to farmers, or just disappear into a black hole. Lots of projects have been done with EU help, but (I guess for political reasons) this has never been well publicized.
So I can see why people voted leave, even though I think it will cause the county to suffer more in the future. I guess that similar factors affected parts of Wales?