A3,
You hit the nail on the head.
Until very recently, "dispatchers" were basically "ambulance"/"fire"/"public safety" comm center workers. Things might vary a bit from operation to operation but as far as being "FAA Licensed" aviation dispatchers they are not.
The FAA did recently require 135 Operators (HEMS) to comply with aircraft dispatch and flight following requirements as set forth by FAR 135. Some operators now have a central "dispatch" office manned by FAA licensed pilots who "track" flights and monitor pre-flight weather decisions.
I flew at one operation where some of the dispatchers were very switched on and would monitor weather for us and several times made a real difference. But again, they were not "FAA Licensed, trained, or rated pilots" but were just very sharp folks.
Perhaps some of the active EMS pilots can describe how their system works.