They get paid. A big part of it is that they have nothing to do with insurance. The amount of effort required to get any kind of payment out of an insurance company is just as insane as trying to get it out of the government for medicare.

It's one of the reasons why medical care is so expensive in the US. Especially when the government only pays a fraction of the actual cost of what is done, forcing the remaining cost to either be absorbed or passed on to other customers.