I have never been involved in a reality TV show (and my job isn't exciting enough for the TV crews to come knocking) so I have to only guess how it works. But I would expect that wearing a microphone doesn't give the doctor much input on which segments to use, and that the doctor wouldn't have been involved in getting permissions from the patients and families.

It's obvious in this case that the show wasn't able to get permission from the family (and, given that the family was surprised; the show wasn't able to contact the family), so they blurred the guy's face and thought that made him unidentifiable. I don't believe the doctor had any influence on that decision.