CNET story states that "Facebook estimates that 4.8 percent are duplicate accounts, 2.4 percent are user-misclassified accounts, and 1.5 percent are undesirable accounts." Some of those face accounts are probably doctors.
Have you tried to search for your doctor on Facebook? Many of them are "hiding" from their patients because they don't want to face an awkward situation where a patient tries to "friend" them. Doctors need to have their privacy too. As a result, some doctors create pseudonyms so they can still connect with family and friends.
Facebook continues to modify their privacy settings, but it's nearly impossible to completely "hide" from the rest of the world unless you have zero friends connected to your account. As soon as you expand your social network, people will be able to find you.
Other physicians are embracing social media and leveraging it for viral marketing, peer-to-peer communication, population health education, and advocacy. These physicians are very visible on Facebook. They're blogging, using Twitter, and putting themselves out there on the Internet.
How about your doctor? I bet that you haven't been able to find him/her on Facebook. If you do find him/her, don't be offended if that person rejects your friend request. It's nothing personal.