Not really true.
Salt Lake City was forbidden by the state from starting their own ambulance service, they instead contract with Southwest (no one gets the logic behind the decision, so don't ask)
Cities such as Midvale, WVC, Draper and some of Sandy have their own, however most parts of the Unified Fire Authority do not have their own. Murray does not have their own.
Gold Cross isn't the monopoly it once was but they still account for a large number of ambulance runs...either #1 or #2 in the valley depending on what kind of volume Southwest is doing with SLC.