Australia has tax funded health care for all. It's not what it used to be, but in emergency everyone is equal. 
There are long waits for elective surgery (which seldom feel elective to a long suffering patient) , those with private insurance usually don't wait. Although Australian private health insurance is hugely expensive and always has out of pocket expenses. 
The tax funded Medicare system means that everyone can be admitted to hospital and receive care in acute of emergency situation.