I worked in a couple of emergency rooms for a total of 6 years, and you aren't wrong. Assuming the care you need can be entirely performed within the ER, then that's a viable strategy so long as you don't intend to re-visit the hospital.

Hospitals are obligated to provide care regardless of your ability to pay in the moment, and of course they often take care of indigent and foreign patients, with the understanding that they won't be able to recoup their costs.

If you don't have your identification on you, then they simply give you a number to call and they usually ask to respond within a few business days because after that, it's harder to get insurance approval.

This all changes if you're admitted to the hospital and need surgery, because I think there's pre-approval required from your insurance carrier. Though since I worked in the ER, my memory is hazy on that.

If they believe you were deceptive and simply refused to be identified, then that is technically illegal, so they will put up your picture and will alert the police if they see you again. But if you never intend to visit the hospital again, it doesn't really matter. No one is going to hunt you down unless you're doing it on such a large scale that it can't be ignored.

This all said, I want to say that I still think it's an unethical thing to do.