It could also be completely possible that the guy was just mentally ill and killed her due to his messed up reasons, Not everything has to be a conspiracy theory. I think it would take more than the killing of an mp by some nutter to swing the vote in the other direction for most people. Myth busted i would say.
This. I think he wanted attention and chose the referendum to do it because he'd get maximum publicity, whereas if he'd murdered her on an ordinary Thursday, there'd have been a few lines in the press and then the story would have moved on to the next thing.