Sorta
That NHS number you've got there is a little out of date. That's from before the Blair/Brown splurge of cash on it. More like 10-11% these days.
But yes, the US medical system is insane. It's so bad that even Stalinist central planning like the NHS would be better.
Better than either would be a more market oriented system like Singapore of course, but that's another matter.
BTW, it's not really the billing etc that costs so much in the US. It's that we actually see that cost. It's there in the accounts of the insurance companies. When a health care system is paid for from taxation the costs of the billing are the reduction in economic activity as a result of the taxation (the "deadweight costs") which of course we never do see.