I'm not surprised at all about that this NBC News.com article identifies south Florida as a hot spot for identity theft by and at health care providers. Time after time staff at Florida hospitals and doctor's offices are in the news for stealing patient's Social Security numbers for identity theft purposes.
Think about it, every time you see a new doctor and fill out an intake form there is a spot for your Social Security number and most people think you have to provide it. "Quick said: 'you do not have to provide your Social Security number, but you do have to provide enough information for you to be distinguishable from other people.'"
I stopped providing my SS number to doctor's offices long ago and from time to time I get some push back on it. A couple of years ago I was trying to make an appointment with a new health care provider, a dermatologist, and the intake person would not give me an appointment unless I gave her my Social Security number. I declined and sought out care from another provider. That has been the only time I had a real problem with declining to provide the number to a health care provider.
If you are utilizing a government health care insurance system, i.e. Medicare, Medicaid the VA, you, unfortunately, have to provide your Social Security number because that is the way those programs identify you. But most private insurance companies no longer utilize Social Security numbers as an identifier and there really is no reason for a doctor to need this information from you except to increase there ability to collect a debt.
This handy list from the IRS provides the situations where there is a legal requirement to fork over your numbers.