This is true unless you can't pay, in which case you will still be treated and the taxpayer will foot the bill under EMTALA.
Note that this only works for emergency room care. Emergency rooms don't provide cancer treatment or dental surgery or lots of other things we consider to be medical problems. And even for problems that the ER will treat, they will only get you stable: so, if you have a heart attack, they'll stabilize you, but they won't put in stents or do any of the followup care that a good cardiologist would do in the weeks after your heart attack.
Note that this only works for emergency room care. Emergency rooms don't provide cancer treatment or dental surgery or lots of other things we consider to be medical problems. And even for problems that the ER will treat, they will only get you stable: so, if you have a heart attack, they'll stabilize you, but they won't put in stents or do any of the followup care that a good cardiologist would do in the weeks after your heart attack.