The way understand it, yes, the uninsured person would receive the $67k bill, but can then go and negotiate to lower the amount payable. Insurance companies just did that negotiation beforehand and have a standing agreement with the provider. All of this reeks of huge inefficiencies to me. There are people at both the insurance companies as well as at every health care service provider whose full time job is to negotiate rates with each other?
I've been in this situation, and there is no comparison at all. Nobody but the very wealthy can afford to pay out of pocket for healthcare. A single, minor injury can cost you $50,000 - $100,000. A chronic condition, cancer treatment, or major surgery can easily head north of $1 million.
Sure, you can try to negotiate pretty much anything. But what kind of leverage do you think you have? Insurance companies can put many millions of dollars of revenue at risk with the threat of dropping a stubborn healthcare provider from their network.
In contrast, your negotiation position is A) please? and B) I may be forced to declare bankruptcy, in which case you may or may not get your money. If you have enough assets, then option B is basically another form of A: "please, don't take away my house or the savings I've spent my life earning." The bigger your bill, the greater the incentive to deal with the annoyance involved in collecting from you. The likely consequence of your personal financial ruin doesn't enter into their calculations.