In my experience these forms are only signed by patients, so why are they valid in those cases?
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.