I think I am the one whose post may have been a bit confusing, I was trying to say I think you have found a reference to something that none of us has ever heard of.
I was at Beauvoir today, I asked the good folks who worked in the gift shop if they knew anything about a Confederated Medical Dept. badge. None of them had ever heard of it either. Not saying one way or the other how much these folks know about the makeup of the CSA army.
I have a couple of more sources I will check with, perhaps they can shed some light on the subject.