And if they swap the form in secret in order to trick surgeons into performing an operation which they haven't agreed to pay for, it's pretty clear that they're committing fraud.
From my understanding, the medical billing system is so fucked precisely because hospitals bought laws making it so they can arbitrarily bill patients without forming a proper contract (otherwise there would be no way to charge someone who was admitted while unconscious). In the absence of such laws they'd have to fall back to an unjust enrichment claim, under which it would be pretty hard to justify charging someone $25 for an aspirin.