In reply to Ava Adore:
As has been said, the race will need to have insurance and you'll be covered for most medical stuff. I think the problem would arise though for instance if you broke a leg, and needed repatriating back to the UK after having surgery - meaning another flight with specialist help. If your insurance stated no to competitive events (many normal policies do) then you might end up paying for this yourself.
Saying that, I've run a few ultras in France without any specific insurance. I'm going to Amsterdam in October for a road marathon and am not going to take any specific insurance.
If I was going to the US for a race I would definitely look into it since the medical costs could get silly very quickly.