What if it’s not an emergency, as defined by EMTALA, but something like cancer? A hospital does have to take you in and stabilize you if you are having a heart attack, but not if you find some hard lump, or persistent low-grade bleeding.
Let that progress until you’ve got a ruptured bowel, or seizures because of the brain tumors - yeah, then they have to stabilize you. But not until then.
A for profit hospital can if the choose tell you to pay or go pound sand
It's only the immediate emergency situation that is scary going without insurance in a world of no pre-conditions.