I would believe that could be the case, at least in some states. But on that front, all of these articles about terrible hospital bills are doing a grace disservice by failing to mention those laws, so that public support can build against them. If anyone were given the power to create legally valid debts out of thin air, they would of course abuse it. Preventing that is one of the main purposes of contract law.
> If anyone were given the power to create legally valid debts out of thin air, they would of course abuse it.
Which, incidentally, does exist in places. E.g., when CO mints a new transportation authority they give a private corporation oversight-free permission to set their own rates and penalties, enforceable by law. That's resulted in a long string of complaints about toll roads charging not just the toll, but for the first bill they never sent, an extra 1000% interest here and there, a fine because they had to "send a second bill," ....