That's exactly what's happening. The insurance company doesn't pay anywhere close to that price. Neither do uninsured people, typically - they just go bankrupt. There's a collusion between hospitals and insurers to help cook each other's books, and to inflate the customer's perception of value.

BTW, if you are uninsured you should negotiate before receiving service, apparently you can get a big discount simply by agreeing to pay ahead of time. Of course that's not really feasible in true emergencies, but you can still negotiate a payment plan.