I was speaking of the US, but I also live in the UK, and I have first-hand experience getting a UK visa as a highly paid professional, and it was not exactly easy. Also I might add that though the NHS is set up as a human right, all public funds are not. For instance, I have to pay for my daughter's school in full, which would be partially covered by the state if I were a citizen. So it's not a question of going from "open" borders to "closed", it's a question of degree.