Not if they understand it might make things worse for the whole country, including them, in the short term, but they believe it will - or might - make things better, especially for them, in the longer term.
If things had carried on exactly as they were before things might be better for the country as a whole but they would still be left behind, their communities would still be completely forgotten, people would have to move to cities in order to have any opportunities.
With Brexit, maybe things get worse for the country as a whole and maybe for that reason things get worse for them in the short term. But in facing up to the problems of Brexit, maybe things change for small towns. I dont think it will happen, by the way, but this is far more debatable, far less predictable, than the immediate fallout and chaos, which is pretty much a certainty as this point. There is at least a chance.
If your circumstances are shit you might as well vote for chaos, because after things have been shaken up there is a chance they will settle again in a way that is more favourable for you. I dont think that is stupid at all.