No, the at fault driver and/or their insurance would be responsible for paying their medical costs. The person who was hit doesn't pay their medical bills and then ask the insurance company for reimbursement. They file a claim with the insurance company to pay their medical bills directly. AFAIK all US states require bodily injury coverage to work that way.
This is not quite true - if your insurance policy does not cover the full amount you can be on the hook.
Of course if you don’t have insurance you’re kind of screwed, or your insurance doesn’t cover the full recovery costs you have to pay the medical bills and get stuck with them if the responsible party is under insured and lacks assets.
Accident created expenses seem like one of those things where if someone else is responsible for the costs you should be able to simply transfer all subsequent costs to them, rather than being stuck with bankruptcy or life long debt if they can’t afford to repay you.
Honestly there should be a transitive debt mechanism - but companies won’t like that because currently they can just force people to settle for some minimal payout knowing that they aren’t on the hook for anything that comes up down the road.
> if your insurance policy does not cover the full amount you can be on the hook.
If "your" means the person who got hit, it's not their insurance that's on the hook, it's the insurance of the person who hit them.
Yes, that person's insurance will have a limit, after which your own insurance coverage for uninsured or under-insured drivers would kick in. And if that also hits a limit, then you would have to sue the party that hit you for damages to get back anything you had to pay over the limit.
> you have to pay the medical bills and get stuck with them if the responsible party is under insured and lacks assets.
In this situation also, yes, once you were over the limit of your own uninsured or under-insured driver coverage, you would have to go to court to get the burden put on the responsible party, so that if that party were judgment proof, it would be the medical provider's problem, not yours.
> if someone else is responsible for the costs you should be able to simply transfer all subsequent costs to them
You can do this, but yes, it does take a lawsuit once you're over whatever limits insurance will cover, as above.
As a non-American, accident created expenses seem like one of those things where the state should cover the personal injury costs which helps to make healthcare cost at least half the price, leads to better outcomes, and avoids people being bankrupted simply because of their health.
> accident created expenses seem like one of those things where the state should cover the personal injury costs
As far as an individual who gets injured by someone else is concerned, "the state" is just another form of insurance. I'm not sure the state is any more reliable as an insurance provider than private companies; indeed, it might often be less so since it is subject to political pressures that private insurance providers are not.