Here in central WV, the hospitals go on diversion when the ER is full. Now, that doesn't mean that they won't take a patient, but the patient's condition will need to correlate with the hospital's specialty. We have three main hospitals in Charleston: Charleston Area Medical Center General Division (level 1 trauma center), CAMC Memorial (specializing in more medical based issues, like heart attacks, strokes, geriatric, etc), and CAMC Women's and Children's Division (self explanatory). So, if Grandma is having chest pains and wants to go to General, and General is on diversion, she goes to Memorial. But if she is a car wreck patient being flown in, then she goes to General. There are other hospitals in the area, but those three are the big players.
I worked as an EMT for a few years, so that all comes from experience.