I'm not sure quite how to read the distinction between Civilian and non-civilian? In King County (Medic One) the FDs have full time designated Medics that are assigned to the Medic Units. Some (maybe even most) came from the Fire ranks but some did not. That being said, I wouldn't consider these guys & gals to be civilian.
I think the distiction has to do with the terms of their employment. Some fire departments employ paramedics in a way similar to a contractor and not a member of the municiple fire service. Not to beat a dead horse but DC was doing that prior to starting their currently incomplete merger. It is also done in parts of IL, with several private agencies "hirng out" ALS memebers.
The long and short of it is, they do not get the same pay and benefits as the Fire fighters but they are not required to have fire training and obviously do not take part in non medical activities such as rescue or suppression.
In places I have seen this in action, the medic is basically a second class employee in all respects. Both in pay and benefits, managerial support, and almost total lack of respect by the municiple firefighters.
As opposed to a firefighter/paramedic who is assigned to a ALS transporting unit full time in the same way a person can be assigned to an engine company, truck company, etc.
If you are going to have a dual role agency, the firefighter/paramedic model with dedicated assignment seems to be a better implementation model.