That's weird, I always thought that American healthcare has good money, since you're paying a lot, for everything.
I would imagine people in our Healthcare system (Czech) use fax somewhere too. But we have healthcare payed from taxes and whole system keeps going only because of nurses and doctors working ridiculous hours for mediocre pay.
If you deal with any sort of government background investigation for getting a job then the chances are high that you will need to send the documents via fax.
My experience has been it's sadly the exception that allows you to digitally upload the required files. Although my experience has only been with Australian, UK and US based companies.
I didn't see anyone using a fax for about 10 years or more.