If you have an HMO, the only time you’re liable for out-of-network bills is if you need a emergency treatment - but then you will covered as soon as transfer can be arranged to an HMO hospital.
HMOs are required, like other Obamacare plans, to reimburse out-of-network hospitals for emergency care (at what the plan considers a “reasonable rate”). But the hospital can pursue ‘balance billing’ against the patient unless state regulations prohibit.