I once saw a bizarrely circular case where a PhD student who was coming to do an internship was refused an academic visitor's visa because the university were paying him a subsistence allowance, and we were told that he needed a work permit, but on applying for the work permit we were told that he didn't qualify because he wouldn't be earning a market rate salary, so we should for an academic visitor's visa instead. He got here in the end, but only because we persuaded the Home Office to write a letter to the embassy who turned down the first visa application - which should actually have been approved because it's legal to pay living/travel expenses for an academic visitor - but we never managed to get a refund on the ~£400 that we paid in application fees. Academic visas are a complete pain in the arse, because most immigration officials don't know they exist, and I've had to read them pages from their own rule book before now.

Despite this, one of my colleagues sincerely believes that anyone can come into the country whenever they like, and that the government will hand them the keys to a council house and a benefits cheque on day one.