Bit of an ignorant take honestly. US medical system is horrible but we absolutely have some of the finest and most advanced teaching hospitals and medical research centers in the world if you're fortunate enough to end up in their care. Mayo clinic, Cleveland Clinic, Massachusetts General, UCLA Health, UC Davis Medical Center, Johns Hopkins Medical Center, Mount Sinai Hospital, the list goes on.
House MD takes place in a fictitious teaching hospital in Princeton, NJ, of Princeton University fame. It is an extremely wealthy area and the reputation and prestige of the hospital is going to be far more important than what the patient can pay.
Also though, no hospital can legally refuse care if you aren't stable, they might just not do much for you other than stabilize you enough to discharge you so you can die somewhere else.
It was never presented as representing a typical patient experience.