Winter, these are excellent points, and ordinarily CERT should be sponsored by the county's Office of Emergency Management; that is the best approach.
I live in Flint, Michigan. If you are aware of the water situation here, it makes it easier to understand the politics involved. In the last 6 years, in an attempt to start a CERT, I have met with two mayors, three police chiefs, a fire chief, the city manager and three county emergency managers. All but two of these have resigned or been fired. The mayor who supported CERT was not reelected.
It wasn't like I was some random citizen off the street making the proposal. I was well known as the captain of the police auxiliary (which I founded) and the Red Cross commo chief for 11 counties, and have extensive training in disaster response. To put it bluntly, CERT is unlikly to be implemented in this county anytime soon. I trust this answers your questions about having separate entities. There wouldn't be.