indeed thats why to have accountants and lawyers, the issue here is that non-dom meant that you could avoid paying tax on stuff you earnt outside of the UK. for example if you have a lot of income being generated in the USA, then being a non-dom meant that you could avoid paying tax here in the UK at the same time.
For US citizens its a bit harder, as you're liable for tax on all income, regardless of source. I'm not sure how they get round that, debt financing or something similar I imagine