In my jurisdiction this is false. (USA near DC). This realt depends on the hospital system. If you come in on an ambulance (with a legitimate illness or injury) you will get placed in a room by EMS and EMS will transfer your care to hospital staff (either a RN or MD) before leaving you. On the rare instance that I have moved a patient to the waiting room at thr request of hospital staff is with a patients that did not need present with any need to be seen.
I have never recommended that a patient can wait, that is outside of my scope of practice and is not advocating for my pt. The extent of my interaction with the hospital is laying out the facts of the pt conditions (vitals,  pertinent medical information, and history)
A lot of places are moving to “soft billing” where you’ll be sent a bill but if you don’t pay it’s written off; or no billing for residents. (Assuming you habe government run EMS and not private)
As an volunteer EMT I hate hearing that a pt doesn’t want to be transported because of the price. Life saving care shouldn’t be cost prohibitive, I’m glad my jurisdiction changed as this became more common.