As others have said, in an emergency situation we treat whoever is the sickest first. If it is not an emergency then it is first come, first served. The patient's financial situation does not factor into the timeliness or quality of care that we provide. No one is turned away from an emergency room based on their ability to pay.
We always strive to give the best care, but that COULD vary from person to person based on finances. If I have a long term relationship with a patient then I will be aware of their financial/insurance status, and I will work with their insurance company and the patient themselves to come up with a plan that works best for them. For example, this might mean that I might have to choose drug B instead of the newer drug A if insurance doesn't cover drug A. We work within our current system to provide the best possible situation for each individual.